********************************************************************************
************** Testing random number generators and distributions **************
********************************************************************************
Using seed: 0x34f05c64d7ad598f

Quality testing basic random number generator cmb_random(), uniform on [0,1)
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.5000	  0.2887	 0.08333	   0.000	  -1.200
1.000e+06	  0.4999	  0.2887	 0.08335	0.0009438	  -1.200
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#################################################=
[   0.05000,     0.1000)   |#################################################=
[    0.1000,     0.1500)   |#################################################-
[    0.1500,     0.2000)   |#################################################=
[    0.2000,     0.2500)   |#################################################=
[    0.2500,     0.3000)   |#################################################=
[    0.3000,     0.3500)   |#################################################-
[    0.3500,     0.4000)   |#################################################=
[    0.4000,     0.4500)   |#################################################-
[    0.4500,     0.5000)   |#################################################=
[    0.5000,     0.5500)   |#################################################-
[    0.5500,     0.6000)   |#################################################=
[    0.6000,     0.6500)   |#################################################=
[    0.6500,     0.7000)   |#################################################=
[    0.7000,     0.7500)   |#################################################-
[    0.7500,     0.8000)   |#################################################-
[    0.8000,     0.8500)   |#################################################-
[    0.8500,     0.9000)   |##################################################
[    0.9000,     0.9500)   |#################################################=
[    0.9500,      1.000)   |#################################################=
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------

Autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.002                                  |-
   2   0.001                                  |-
   3  -0.001                                 -|
   4   0.001                                  |-
   5   0.000                                  |-
   6  -0.000                                 -|
   7  -0.002                                 -|
   8   0.000                                  |-
   9  -0.000                                 -|
  10  -0.000                                 -|
  11   0.001                                  |-
  12   0.001                                  |-
  13  -0.000                                 -|
  14  -0.001                                 -|
  15  -0.000                                 -|
--------------------------------------------------------------------------------

Partial autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.002                                  |-
   2   0.001                                  |-
   3  -0.001                                 -|
   4   0.001                                  |-
   5   0.000                                  |-
   6  -0.000                                 -|
   7  -0.002                                 -|
   8   0.000                                  |-
   9  -0.000                                 -|
  10  -0.000                                 -|
  11   0.001                                  |-
  12   0.001                                  |-
  13  -0.000                                 -|
  14  -0.001                                 -|
  15  -0.000                                 -|
--------------------------------------------------------------------------------

Raw moment:   Expected:   Actual:   Error:
--------------------------------------------------------------------------------
    1             0.5     0.49992   -0.016 %
    2         0.33333     0.33327   -0.020 %
    3            0.25     0.24996   -0.014 %
    4             0.2     0.19999   -0.006 %
    5         0.16667     0.16667    0.004 %
    6         0.14286     0.14288    0.013 %
    7           0.125     0.12503    0.020 %
    8         0.11111     0.11114    0.026 %
    9             0.1     0.10003    0.030 %
   10        0.090909    0.090939    0.032 %
   11        0.083333    0.083361    0.033 %
   12        0.076923    0.076948    0.032 %
   13        0.071429     0.07145    0.030 %
   14        0.066667    0.066685    0.028 %
   15          0.0625    0.062515    0.024 %
--------------------------------------------------------------------------------
Testing Goodness of Fit vs the U(0,1) distribution
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  11.5          15    Sigma:  -0.57  Odds: 1 in    1.8    
Neyman's smooth test                        4.67          10    Sigma:  -1.36  Odds: 1 in    5.7    
    Neyman V1: mean                       -0.269           0    Sigma:  -0.27  Odds: 1 in    1.3    
    Neyman V2: variance                    0.184           0    Sigma:  +0.18  Odds: 1 in    1.2    
    Neyman V3: skewness                    0.779           0    Sigma:  +0.78  Odds: 1 in    2.3    
    Neyman V4: kurtosis                   -0.139           0    Sigma:  -0.14  Odds: 1 in    1.1    
    Neyman remainder: fine structure         271         251    Sigma:  +0.89  Odds: 1 in    2.7    
Anderson-Darling EDF test                  0.291           1    Sigma:  -1.59  Odds: 1 in    9.0    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +1.22  Odds: 1 in    4.5    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing cmb_random_uniform(-1,2)
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.5000	  0.8660	  0.7500	   0.000	  -1.200
1.000e+06	  0.5000	  0.8658	  0.7496	0.001048	  -1.200
--------------------------------------------------------------------------------
( -Infinity,     -1.000)   |
[    -1.000,    -0.8000)   |#################################################=
[   -0.8000,    -0.6000)   |#################################################=
[   -0.6000,    -0.4000)   |#################################################=
[   -0.4000,    -0.2000)   |#################################################=
[   -0.2000,      0.000)   |#################################################=
[     0.000,     0.2000)   |#################################################=
[    0.2000,     0.4000)   |#################################################=
[    0.4000,     0.6000)   |#################################################=
[    0.6000,     0.8000)   |#################################################=
[    0.8000,      1.000)   |##################################################
[     1.000,      1.200)   |#################################################=
[     1.200,      1.400)   |#################################################=
[     1.400,      1.600)   |#################################################=
[     1.600,      1.800)   |#################################################=
[     1.800,      2.000)   |#################################################=
[     2.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  10.8          15    Sigma:  -0.73  Odds: 1 in    2.2    
Neyman's smooth test                        6.09          10    Sigma:  -0.87  Odds: 1 in    2.6    
    Neyman V1: mean                      0.00253           0    Sigma:  +0.00  Odds: 1 in    1.0    
    Neyman V2: variance                   -0.593           0    Sigma:  -0.59  Odds: 1 in    1.8    
    Neyman V3: skewness                     1.35           0    Sigma:  +1.35  Odds: 1 in    5.7    
    Neyman V4: kurtosis                   -0.476           0    Sigma:  -0.48  Odds: 1 in    1.6    
    Neyman remainder: fine structure         244         251    Sigma:  -0.29  Odds: 1 in    1.3    
Anderson-Darling EDF test                  0.359           1    Sigma:  -1.22  Odds: 1 in    4.5    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.76  Odds: 1 in    2.2    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing cmb_random_triangular(-1, 2, 3)
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.333	  0.8498	  0.7222	 -0.4224	 -0.6000
1.000e+06	   1.334	  0.8503	  0.7231	 -0.4218	 -0.6007
--------------------------------------------------------------------------------
( -Infinity,     -1.000)   |
[    -1.000,    -0.8000)   |#=
[   -0.8000,    -0.6000)   |#####-
[   -0.6000,    -0.4000)   |########=
[   -0.4000,    -0.2000)   |###########=
[   -0.2000,      0.000)   |###############=
[     0.000,     0.2000)   |##################=
[    0.2000,     0.4000)   |######################-
[    0.4000,     0.6000)   |##########################-
[    0.6000,     0.8000)   |#############################-
[    0.8000,      1.000)   |################################-
[     1.000,      1.200)   |####################################-
[     1.200,      1.400)   |#######################################=
[     1.400,      1.600)   |###########################################-
[     1.600,      1.800)   |##############################################-
[     1.800,      2.000)   |##################################################
[     2.000,      2.200)   |##############################################-
[     2.200,      2.400)   |####################################-
[     2.400,      2.600)   |##########################-
[     2.600,      2.800)   |###############=
[     2.800,      3.000)   |#####-
[     3.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  21.9          15    Sigma:  +1.22  Odds: 1 in    4.5    
Neyman's smooth test                          11          10    Sigma:  +0.37  Odds: 1 in    1.4    
    Neyman V1: mean                        0.342           0    Sigma:  +0.34  Odds: 1 in    1.4    
    Neyman V2: variance                     1.11           0    Sigma:  +1.11  Odds: 1 in    3.7    
    Neyman V3: skewness                    0.927           0    Sigma:  +0.93  Odds: 1 in    2.8    
    Neyman V4: kurtosis                     1.35           0    Sigma:  +1.35  Odds: 1 in    5.6    
    Neyman remainder: fine structure         229         251    Sigma:  -0.98  Odds: 1 in    3.1    
Anderson-Darling EDF test                  0.796           1    Sigma:  +0.04  Odds: 1 in    1.0    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing standard normal distribution, mean = 0, sigma = 1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   0.000	   1.000	   1.000	   0.000	   0.000
1.000e+06	0.0005126	  0.9994	  0.9988	0.003536	-0.001614
--------------------------------------------------------------------------------
( -Infinity,     -5.000)   |
[    -5.000,     -4.000)   |-
[    -4.000,     -3.000)   |-
[    -3.000,     -2.000)   |###-
[    -2.000,     -1.000)   |###################=
[    -1.000,      0.000)   |##################################################
[     0.000,      1.000)   |#################################################=
[     1.000,      2.000)   |###################=
[     2.000,      3.000)   |###-
[     3.000,      4.000)   |-
[     4.000,      5.000)   |-
[     5.000,      6.000)   |-
[     6.000,   Infinity)   |
--------------------------------------------------------------------------------

Autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.004                                  |-
   2   0.002                                  |-
   3  -0.000                                 -|
   4  -0.000                                 -|
   5  -0.000                                 -|
   6  -0.001                                 -|
   7   0.000                                  |-
   8  -0.000                                 -|
   9  -0.001                                 -|
  10   0.001                                  |-
  11  -0.000                                 -|
  12  -0.000                                 -|
  13   0.000                                  |-
  14   0.001                                  |-
  15  -0.001                                 -|
--------------------------------------------------------------------------------

Partial autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.004                                  |-
   2   0.002                                  |-
   3  -0.000                                 -|
   4  -0.000                                 -|
   5  -0.000                                 -|
   6  -0.001                                 -|
   7   0.000                                  |-
   8  -0.000                                 -|
   9  -0.001                                 -|
  10   0.001                                  |-
  11  -0.000                                 -|
  12  -0.000                                 -|
  13   0.000                                  |-
  14   0.001                                  |-
  15  -0.001                                 -|
--------------------------------------------------------------------------------

                              Cimba ziggurat method:    Box Muller method:
Raw moment:     Expected:     Actual:     Error:        Actual:     Error:
--------------------------------------------------------------------------------
    1                 0     0.0005126      ---        0.0004222      ---
    2                 1        0.9988   -0.121 %          1.002    0.185 %
    3                 0      0.005065      ---         0.002557      ---
    4                 3         2.991   -0.295 %          3.009    0.305 %
    5                 0       0.04681      ---         0.005491      ---
    6                15         14.94   -0.414 %          15.08    0.512 %
    7                 0        0.6381      ---          -0.1755      ---
    8               105         104.9   -0.138 %          105.9    0.811 %
    9                 0         11.09      ---           -5.454      ---
   10               945         953.8    0.929 %          956.8    1.247 %
   11                 0         219.2      ---           -130.1      ---
   12          1.04e+04     1.072e+04    3.117 %      1.061e+04    2.101 %
   13                 0          4698      ---            -3070      ---
   14         1.351e+05      1.44e+05    6.568 %      1.404e+05    3.880 %
   15                 0     1.071e+05      ---       -7.536e+04      ---
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  7.33          15    Sigma:  -1.62  Odds: 1 in    9.6    
Neyman's smooth test                        12.4          10    Sigma:  +0.64  Odds: 1 in    1.9    
    Neyman V1: mean                       -0.185           0    Sigma:  -0.19  Odds: 1 in    1.2    
    Neyman V2: variance                    -0.66           0    Sigma:  -0.66  Odds: 1 in    2.0    
    Neyman V3: skewness                    -1.56           0    Sigma:  -1.56  Odds: 1 in    8.3    
    Neyman V4: kurtosis                    0.215           0    Sigma:  +0.22  Odds: 1 in    1.2    
    Neyman remainder: fine structure         209         251    Sigma:  -1.98  Odds: 1 in    21.    
Anderson-Darling EDF test                  0.382           1    Sigma:  -1.11  Odds: 1 in    3.7    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.62  Odds: 1 in    1.9    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Binomial tail test, standard normal, n = 10000000
t        expected      obs (zig)      deficit      sigma      obs (B-M)      deficit      sigma
0.0005         3989.4         4023    -0.8417%       0.53         3960     0.7375%      -0.47
0.0010         7978.8         7977     0.0231%      -0.02         8011    -0.4030%       0.36
0.0050        39894.1        40027    -0.3332%       0.67        39881     0.0327%      -0.07
0.0100        79787.1        79982    -0.2442%       0.69        80016    -0.2869%       0.81
0.0200       159566.3       159927    -0.2261%       0.91       159743    -0.1108%       0.45
0.0300       239329.5       239548    -0.0913%       0.45       239809    -0.2004%       0.99
0.0400       319068.7       319142    -0.0230%       0.13       319211    -0.0446%       0.26
0.0500       398776.1       398718     0.0146%      -0.09       398725     0.0128%      -0.08
0.0600       478443.7       478139     0.0637%      -0.45       478654    -0.0440%       0.31
0.0800       637627.4       637301     0.0512%      -0.42       637630    -0.0004%       0.00
0.1000       796556.7       796428     0.0162%      -0.15       797443    -0.1113%       1.04

Quality testing normal distribution, mean = 2.000000, sigma = 1.000000
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   2.000	   1.000	   1.000	   0.000	   0.000
1.000e+06	   1.998	  0.9999	  0.9999	-0.0005153	-0.01098
--------------------------------------------------------------------------------
( -Infinity,     -3.000)   |
[    -3.000,     -2.500)   |-
[    -2.500,     -2.000)   |-
[    -2.000,     -1.500)   |-
[    -1.500,     -1.000)   |-
[    -1.000,    -0.5000)   |#-
[   -0.5000,      0.000)   |####-
[     0.000,     0.5000)   |###########=
[    0.5000,      1.000)   |########################-
[     1.000,      1.500)   |#######################################-
[     1.500,      2.000)   |#################################################=
[     2.000,      2.500)   |##################################################
[     2.500,      3.000)   |#######################################-
[     3.000,      3.500)   |#######################=
[     3.500,      4.000)   |###########=
[     4.000,      4.500)   |####-
[     4.500,      5.000)   |#-
[     5.000,      5.500)   |-
[     5.500,      6.000)   |-
[     6.000,      6.500)   |-
[     6.500,      7.000)   |-
[     7.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  10.6          15    Sigma:  -0.77  Odds: 1 in    2.3    
Neyman's smooth test                        9.16          10    Sigma:  -0.04  Odds: 1 in    1.0    
    Neyman V1: mean                         1.77           0    Sigma:  +1.77  Odds: 1 in    13.    
    Neyman V2: variance                    0.814           0    Sigma:  +0.81  Odds: 1 in    2.4    
    Neyman V3: skewness                    0.532           0    Sigma:  +0.53  Odds: 1 in    1.7    
    Neyman V4: kurtosis                    -0.51           0    Sigma:  -0.51  Odds: 1 in    1.6    
    Neyman remainder: fine structure         247         251    Sigma:  -0.16  Odds: 1 in    1.1    
Anderson-Darling EDF test                   1.82           1    Sigma:  +1.20  Odds: 1 in    4.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.73  Odds: 1 in    2.2    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing standard exponential distribution, mean = 1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.000	   1.000	   1.000	   2.000	   6.000
1.000e+06	  0.9994	  0.9989	  0.9978	   2.007	   6.059
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |##################################################
[     1.000,      2.000)   |##################-
[     2.000,      3.000)   |######=
[     3.000,      4.000)   |##-
[     4.000,      5.000)   |=
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |-
[     13.00,      14.00)   |-
[     14.00,   Infinity)   |
--------------------------------------------------------------------------------

Autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.000                                  |-
   2   0.001                                  |-
   3  -0.001                                 -|
   4  -0.001                                 -|
   5  -0.002                                 -|
   6   0.001                                  |-
   7   0.000                                  |-
   8   0.003                                  |-
   9   0.000                                  |-
  10   0.001                                  |-
  11  -0.002                                 -|
  12   0.001                                  |-
  13  -0.000                                 -|
  14  -0.000                                 -|
  15  -0.001                                 -|
--------------------------------------------------------------------------------

Partial autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.000                                  |-
   2   0.001                                  |-
   3  -0.001                                 -|
   4  -0.001                                 -|
   5  -0.002                                 -|
   6   0.001                                  |-
   7   0.000                                  |-
   8   0.003                                  |-
   9   0.000                                  |-
  10   0.001                                  |-
  11  -0.002                                 -|
  12   0.001                                  |-
  13  -0.000                                 -|
  14  -0.000                                 -|
  15  -0.001                                 -|
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  16.7          15    Sigma:  +0.43  Odds: 1 in    1.5    
Neyman's smooth test                        11.8          10    Sigma:  +0.52  Odds: 1 in    1.7    
    Neyman V1: mean                         0.35           0    Sigma:  +0.35  Odds: 1 in    1.4    
    Neyman V2: variance                     -2.5           0    Sigma:  -2.50  Odds: 1 in    81.    
    Neyman V3: skewness                    0.304           0    Sigma:  +0.30  Odds: 1 in    1.3    
    Neyman V4: kurtosis                   -0.451           0    Sigma:  -0.45  Odds: 1 in    1.5    
    Neyman remainder: fine structure         240         251    Sigma:  -0.48  Odds: 1 in    1.6    
Anderson-Darling EDF test                   1.34           1    Sigma:  +0.78  Odds: 1 in    2.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.16  Odds: 1 in    1.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Binomial tail test, standard exponential, n = 10000000
t        expected      obs (zig)      deficit      sigma      obs (inv)      deficit      sigma
0.001          4998.8         4987     0.2351%      -0.17         5150    -3.0258%       2.14
0.001          9995.0         9918     0.7704%      -0.77        10164    -1.6908%       1.69
0.005         49875.2        49642     0.4676%      -1.05        49855     0.0405%      -0.09
0.010         99501.7        99522    -0.0204%       0.06        99247     0.2559%      -0.81
0.020        198013.3       197633     0.1920%      -0.86       197561     0.2284%      -1.03
0.030        295544.7       294895     0.2198%      -1.21       294919     0.2117%      -1.17
0.040        392105.6       391463     0.1639%      -1.05       391997     0.0277%      -0.18
0.050        487705.8       486690     0.2083%      -1.49       487751    -0.0093%       0.07
0.060        582354.7       581695     0.1133%      -0.89       581434     0.1581%      -1.24
0.080        768836.5       768267     0.0741%      -0.68       767298     0.2001%      -1.83
0.100        951625.8       951055     0.0600%      -0.62       949928     0.1784%      -1.83

Quality testing exponential distribution, mean = 2.000000
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   2.000	   2.000	   4.000	   2.000	   6.000
1.000e+06	   1.998	   1.997	   3.989	   1.993	   5.916
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##################################################
[     2.000,      4.000)   |##################-
[     4.000,      6.000)   |######=
[     6.000,      8.000)   |##-
[     8.000,      10.00)   |=
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |-
[     28.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  5.05          15    Sigma:  -2.40  Odds: 1 in    60.    
Neyman's smooth test                        8.68          10    Sigma:  -0.16  Odds: 1 in    1.1    
    Neyman V1: mean                         -1.2           0    Sigma:  -1.20  Odds: 1 in    4.3    
    Neyman V2: variance                   -0.076           0    Sigma:  -0.08  Odds: 1 in    1.1    
    Neyman V3: skewness                    0.384           0    Sigma:  +0.38  Odds: 1 in    1.4    
    Neyman V4: kurtosis                   -0.931           0    Sigma:  -0.93  Odds: 1 in    2.8    
    Neyman remainder: fine structure         225         251    Sigma:  -1.16  Odds: 1 in    4.1    
Anderson-Darling EDF test                  0.841           1    Sigma:  +0.12  Odds: 1 in    1.1    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing exponential distribution, mean = 0.010000
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	 0.01000	 0.01000	0.0001000	   2.000	   6.000
1.000e+06	0.009998	0.009986	9.973e-05	   1.994	   5.961
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.01000)   |##################################################
[   0.01000,    0.02000)   |##################-
[   0.02000,    0.03000)   |######=
[   0.03000,    0.04000)   |##-
[   0.04000,    0.05000)   |=
[   0.05000,    0.06000)   |-
[   0.06000,    0.07000)   |-
[   0.07000,    0.08000)   |-
[   0.08000,    0.09000)   |-
[   0.09000,     0.1000)   |-
[    0.1000,     0.1100)   |-
[    0.1100,     0.1200)   |-
[    0.1200,     0.1300)   |-
[    0.1300,     0.1400)   |-
[    0.1400,     0.1500)   |-
[    0.1500,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  16.1          15    Sigma:  +0.33  Odds: 1 in    1.3    
Neyman's smooth test                        10.4          10    Sigma:  +0.24  Odds: 1 in    1.2    
    Neyman V1: mean                        0.375           0    Sigma:  +0.38  Odds: 1 in    1.4    
    Neyman V2: variance                     -1.4           0    Sigma:  -1.40  Odds: 1 in    6.2    
    Neyman V3: skewness                      1.7           0    Sigma:  +1.70  Odds: 1 in    11.    
    Neyman V4: kurtosis                   -0.443           0    Sigma:  -0.44  Odds: 1 in    1.5    
    Neyman remainder: fine structure         255         251    Sigma:  +0.23  Odds: 1 in    1.2    
Anderson-Darling EDF test                  0.929           1    Sigma:  +0.26  Odds: 1 in    1.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing exponential distribution, mean = 1000000.000000
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	1.000e+06	1.000e+06	1.000e+12	   2.000	   6.000
1.000e+06	1.000e+06	1.000e+06	1.000e+12	   2.009	   6.103
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,  6.823e+05)   |##################################################-
[ 6.823e+05,  1.365e+06)   |#########################-
[ 1.365e+06,  2.047e+06)   |############=
[ 2.047e+06,  2.729e+06)   |######-
[ 2.729e+06,  3.411e+06)   |###-
[ 3.411e+06,  4.094e+06)   |#=
[ 4.094e+06,  4.776e+06)   |=
[ 4.776e+06,  5.458e+06)   |-
[ 5.458e+06,  6.140e+06)   |-
[ 6.140e+06,  6.823e+06)   |-
[ 6.823e+06,  7.505e+06)   |-
[ 7.505e+06,  8.187e+06)   |-
[ 8.187e+06,  8.870e+06)   |-
[ 8.870e+06,  9.552e+06)   |-
[ 9.552e+06,  1.023e+07)   |-
[ 1.023e+07,  1.092e+07)   |-
[ 1.092e+07,  1.160e+07)   |-
[ 1.160e+07,  1.228e+07)   |-
[ 1.228e+07,  1.296e+07)   |-
[ 1.296e+07,  1.365e+07)   |-
[ 1.365e+07,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  13.2          15    Sigma:  -0.22  Odds: 1 in    1.2    
Neyman's smooth test                        12.1          10    Sigma:  +0.59  Odds: 1 in    1.8    
    Neyman V1: mean                        0.673           0    Sigma:  +0.67  Odds: 1 in    2.0    
    Neyman V2: variance                    -1.15           0    Sigma:  -1.15  Odds: 1 in    4.0    
    Neyman V3: skewness                   -0.355           0    Sigma:  -0.35  Odds: 1 in    1.4    
    Neyman V4: kurtosis                    0.965           0    Sigma:  +0.96  Odds: 1 in    3.0    
    Neyman remainder: fine structure         292         251    Sigma:  +1.77  Odds: 1 in    13.    
Anderson-Darling EDF test                  0.646           1    Sigma:  -0.27  Odds: 1 in    1.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing cmb_random_erlang(5, 1)
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   5.000	   2.236	   5.000	  0.8944	   1.200
1.000e+06	   5.000	   2.234	   4.990	  0.8904	   1.170
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |#######=
[     2.000,      4.000)   |##############################################-
[     4.000,      6.000)   |##################################################
[     6.000,      8.000)   |##########################=
[     8.000,      10.00)   |##########-
[     10.00,      12.00)   |###-
[     12.00,      14.00)   |=
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |
[     24.00,      26.00)   |-
[     26.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  10.1          15    Sigma:  -0.90  Odds: 1 in    2.7    
Neyman's smooth test                        6.29          10    Sigma:  -0.81  Odds: 1 in    2.4    
    Neyman V1: mean                       0.0537           0    Sigma:  +0.05  Odds: 1 in    1.0    
    Neyman V2: variance                    -1.34           0    Sigma:  -1.34  Odds: 1 in    5.6    
    Neyman V3: skewness                    0.571           0    Sigma:  +0.57  Odds: 1 in    1.8    
    Neyman V4: kurtosis                    0.678           0    Sigma:  +0.68  Odds: 1 in    2.0    
    Neyman remainder: fine structure         253         251    Sigma:  +0.14  Odds: 1 in    1.1    
Anderson-Darling EDF test                  0.497           1    Sigma:  -0.67  Odds: 1 in    2.0    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.20  Odds: 1 in    1.2    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing cmb_random_hypoexponential, k = 4, m = [1, 2, 4, 8]
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   15.00	   9.220	   85.00	   1.493	   ---  
1.000e+06	   15.00	   9.224	   85.08	   1.495	   3.629
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      7.000)   |######################=
[     7.000,      14.00)   |##################################################
[     14.00,      21.00)   |################################-
[     21.00,      28.00)   |###############=
[     28.00,      35.00)   |######=
[     35.00,      42.00)   |##=
[     42.00,      49.00)   |#-
[     49.00,      56.00)   |=
[     56.00,      63.00)   |-
[     63.00,      70.00)   |-
[     70.00,      77.00)   |-
[     77.00,      84.00)   |-
[     84.00,      91.00)   |-
[     91.00,      98.00)   |-
[     98.00,      105.0)   |-
[     105.0,      112.0)   |-
[     112.0,      119.0)   |
[     119.0,      126.0)   |-
[     126.0,      133.0)   |
[     133.0,      140.0)   |-
[     140.0,   Infinity)   |
--------------------------------------------------------------------------------

Quality testing cmb_random_hyperexponential, k = 4, m = [1, 2, 4, 8], p = [0.1, 0.2, 0.3, 0.4]
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   4.900	   6.212	   38.59	   ---  	   ---  
1.000e+06	   4.895	   6.208	   38.54	   2.777	   11.47
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      6.000)   |##################################################
[     6.000,      12.00)   |##########=
[     12.00,      18.00)   |####-
[     18.00,      24.00)   |#=
[     24.00,      30.00)   |=
[     30.00,      36.00)   |-
[     36.00,      42.00)   |-
[     42.00,      48.00)   |-
[     48.00,      54.00)   |-
[     54.00,      60.00)   |-
[     60.00,      66.00)   |-
[     66.00,      72.00)   |-
[     72.00,      78.00)   |-
[     78.00,      84.00)   |-
[     84.00,      90.00)   |-
[     90.00,      96.00)   |-
[     96.00,      102.0)   |-
[     102.0,      108.0)   |-
[     108.0,   Infinity)   |
--------------------------------------------------------------------------------

Quality testing cmb_random_weibull(2, 3)
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   2.659	   1.390	   1.931	   ---  	   ---  
1.000e+06	   2.658	   1.391	   1.935	  0.6354	  0.2546
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |###################-
[     1.000,      2.000)   |##############################################-
[     2.000,      3.000)   |##################################################
[     3.000,      4.000)   |####################################-
[     4.000,      5.000)   |###################-
[     5.000,      6.000)   |#######=
[     6.000,      7.000)   |##=
[     7.000,      8.000)   |=
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  13.7          15    Sigma:  -0.13  Odds: 1 in    1.1    
Neyman's smooth test                        11.8          10    Sigma:  +0.54  Odds: 1 in    1.7    
    Neyman V1: mean                        -1.21           0    Sigma:  -1.21  Odds: 1 in    4.4    
    Neyman V2: variance                    0.612           0    Sigma:  +0.61  Odds: 1 in    1.9    
    Neyman V3: skewness                    0.488           0    Sigma:  +0.49  Odds: 1 in    1.6    
    Neyman V4: kurtosis                     1.91           0    Sigma:  +1.91  Odds: 1 in    18.    
    Neyman remainder: fine structure         261         251    Sigma:  +0.48  Odds: 1 in    1.6    
Anderson-Darling EDF test                   1.32           1    Sigma:  +0.75  Odds: 1 in    2.2    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.11  Odds: 1 in    1.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing gamma distribution, shape 3, scale 0.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.500	  0.8660	  0.7500	   1.155	   2.000
1.000e+06	   1.499	  0.8656	  0.7493	   1.154	   1.986
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |###############=
[    0.5000,      1.000)   |################################################-
[     1.000,      1.500)   |##################################################
[     1.500,      2.000)   |####################################=
[     2.000,      2.500)   |######################-
[     2.500,      3.000)   |############-
[     3.000,      3.500)   |######-
[     3.500,      4.000)   |###-
[     4.000,      4.500)   |#-
[     4.500,      5.000)   |=
[     5.000,      5.500)   |-
[     5.500,      6.000)   |-
[     6.000,      6.500)   |-
[     6.500,      7.000)   |-
[     7.000,      7.500)   |-
[     7.500,      8.000)   |-
[     8.000,      8.500)   |-
[     8.500,      9.000)   |-
[     9.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  10.3          15    Sigma:  -0.84  Odds: 1 in    2.5    
Neyman's smooth test                        5.11          10    Sigma:  -1.19  Odds: 1 in    4.3    
    Neyman V1: mean                       -0.956           0    Sigma:  -0.96  Odds: 1 in    3.0    
    Neyman V2: variance                   -0.322           0    Sigma:  -0.32  Odds: 1 in    1.3    
    Neyman V3: skewness                   -0.257           0    Sigma:  -0.26  Odds: 1 in    1.3    
    Neyman V4: kurtosis                    0.752           0    Sigma:  +0.75  Odds: 1 in    2.2    
    Neyman remainder: fine structure         255         251    Sigma:  +0.19  Odds: 1 in    1.2    
Anderson-Darling EDF test                  0.694           1    Sigma:  -0.16  Odds: 1 in    1.1    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.73  Odds: 1 in    2.2    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing gamma distribution, shape 1, scale 1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.000	   1.000	   1.000	   2.000	   6.000
1.000e+06	   1.001	  0.9987	  0.9975	   1.982	   5.815
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |##################################################
[     1.000,      2.000)   |##################-
[     2.000,      3.000)   |######=
[     3.000,      4.000)   |##-
[     4.000,      5.000)   |=
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |-
[     13.00,      14.00)   |-
[     14.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  21.1          15    Sigma:  +1.11  Odds: 1 in    3.8    
Neyman's smooth test                        11.6          10    Sigma:  +0.48  Odds: 1 in    1.6    
    Neyman V1: mean                         1.22           0    Sigma:  +1.22  Odds: 1 in    4.5    
    Neyman V2: variance                    0.208           0    Sigma:  +0.21  Odds: 1 in    1.2    
    Neyman V3: skewness                   -0.823           0    Sigma:  -0.82  Odds: 1 in    2.4    
    Neyman V4: kurtosis                    -0.67           0    Sigma:  -0.67  Odds: 1 in    2.0    
    Neyman remainder: fine structure         292         251    Sigma:  +1.75  Odds: 1 in    13.    
Anderson-Darling EDF test                   1.14           1    Sigma:  +0.55  Odds: 1 in    1.7    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing gamma distribution, shape 0.5, scale 2
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.000	   1.414	   2.000	   2.828	   12.00
1.000e+06	  0.9992	   1.413	   1.998	   2.826	   12.00
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##################################################
[     2.000,      4.000)   |######=
[     4.000,      6.000)   |#=
[     6.000,      8.000)   |=
[     8.000,      10.00)   |-
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |
[     26.00,      28.00)   |-
[     28.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  19.4          15    Sigma:  +0.85  Odds: 1 in    2.5    
Neyman's smooth test                        8.56          10    Sigma:  -0.19  Odds: 1 in    1.2    
    Neyman V1: mean                       -0.615           0    Sigma:  -0.62  Odds: 1 in    1.9    
    Neyman V2: variance                   -0.444           0    Sigma:  -0.44  Odds: 1 in    1.5    
    Neyman V3: skewness                    0.399           0    Sigma:  +0.40  Odds: 1 in    1.4    
    Neyman V4: kurtosis                     0.67           0    Sigma:  +0.67  Odds: 1 in    2.0    
    Neyman remainder: fine structure         288         251    Sigma:  +1.59  Odds: 1 in    8.9    
Anderson-Darling EDF test                  0.513           1    Sigma:  -0.62  Odds: 1 in    1.9    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing gamma distribution, shape 0.1, scale 2
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.2000	  0.6325	  0.4000	   6.325	   60.00
1.000e+06	  0.2001	  0.6323	  0.3998	   6.319	   59.44
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |#################################################=
[     1.000,      2.000)   |#=
[     2.000,      3.000)   |=
[     3.000,      4.000)   |-
[     4.000,      5.000)   |-
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |-
[     13.00,      14.00)   |-
[     14.00,      15.00)   |-
[     15.00,      16.00)   |-
[     16.00,      17.00)   |
[     17.00,      18.00)   |-
[     18.00,      19.00)   |
[     19.00,      20.00)   |-
[     20.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  8.67          15    Sigma:  -1.25  Odds: 1 in    4.7    
Neyman's smooth test                        5.79          10    Sigma:  -0.97  Odds: 1 in    3.0    
    Neyman V1: mean                        0.774           0    Sigma:  +0.77  Odds: 1 in    2.3    
    Neyman V2: variance                    0.864           0    Sigma:  +0.86  Odds: 1 in    2.6    
    Neyman V3: skewness                   -0.526           0    Sigma:  -0.53  Odds: 1 in    1.7    
    Neyman V4: kurtosis                   -0.437           0    Sigma:  -0.44  Odds: 1 in    1.5    
    Neyman remainder: fine structure         255         251    Sigma:  +0.23  Odds: 1 in    1.2    
Anderson-Darling EDF test                  0.646           1    Sigma:  -0.27  Odds: 1 in    1.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.43  Odds: 1 in    1.5    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing log-normal distribution, m 1, s 0.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   3.080	   1.642	   2.695	   1.750	   5.898
1.000e+06	   3.078	   1.640	   2.689	   1.758	   5.995
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##########################-
[     2.000,      4.000)   |##################################################
[     4.000,      6.000)   |###############=
[     6.000,      8.000)   |####-
[     8.000,      10.00)   |#-
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |
[     28.00,      30.00)   |-
[     30.00,      32.00)   |
[     32.00,      34.00)   |
[     34.00,      36.00)   |
[     36.00,      38.00)   |-
[     38.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  15.2          15    Sigma:  +0.17  Odds: 1 in    1.2    
Neyman's smooth test                        10.8          10    Sigma:  +0.33  Odds: 1 in    1.3    
    Neyman V1: mean                        -1.39           0    Sigma:  -1.39  Odds: 1 in    6.1    
    Neyman V2: variance                     -1.1           0    Sigma:  -1.10  Odds: 1 in    3.7    
    Neyman V3: skewness                   -0.803           0    Sigma:  -0.80  Odds: 1 in    2.4    
    Neyman V4: kurtosis                   -0.195           0    Sigma:  -0.20  Odds: 1 in    1.2    
    Neyman remainder: fine structure         275         251    Sigma:  +1.08  Odds: 1 in    3.6    
Anderson-Darling EDF test                   1.33           1    Sigma:  +0.77  Odds: 1 in    2.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.14  Odds: 1 in    1.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing logistic distribution, m 1, s 0.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.000	  0.9069	  0.8225	   0.000	   1.200
1.000e+06	   1.001	  0.9083	  0.8250	0.002107	   1.194
--------------------------------------------------------------------------------
( -Infinity,     -6.000)   |
[    -6.000,     -5.000)   |-
[    -5.000,     -4.000)   |-
[    -4.000,     -3.000)   |-
[    -3.000,     -2.000)   |-
[    -2.000,     -1.000)   |##-
[    -1.000,      0.000)   |#############-
[     0.000,      1.000)   |##################################################
[     1.000,      2.000)   |#################################################=
[     2.000,      3.000)   |#############-
[     3.000,      4.000)   |##-
[     4.000,      5.000)   |-
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  14.7          15    Sigma:  +0.07  Odds: 1 in    1.1    
Neyman's smooth test                        10.8          10    Sigma:  +0.32  Odds: 1 in    1.3    
    Neyman V1: mean                        0.843           0    Sigma:  +0.84  Odds: 1 in    2.5    
    Neyman V2: variance                     1.57           0    Sigma:  +1.57  Odds: 1 in    8.5    
    Neyman V3: skewness                    0.542           0    Sigma:  +0.54  Odds: 1 in    1.7    
    Neyman V4: kurtosis                    0.966           0    Sigma:  +0.97  Odds: 1 in    3.0    
    Neyman remainder: fine structure         236         251    Sigma:  -0.67  Odds: 1 in    2.0    
Anderson-Darling EDF test                   1.05           1    Sigma:  +0.44  Odds: 1 in    1.5    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing cauchy distribution, m 1, s 0.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   ---  	   ---  	   ---  	   ---  	   ---  
1.000e+06	   4.620	   3510.	1.232e+07	   996.9	9.959e+05
--------------------------------------------------------------------------------
( -Infinity, -1.789e+05)   |
[-1.789e+05,      0.000)   |########=
[     0.000,  1.789e+05)   |##################################################
[ 1.789e+05,  3.578e+05)   |
[ 3.578e+05,  5.367e+05)   |
[ 5.367e+05,  7.155e+05)   |
[ 7.155e+05,  8.944e+05)   |
[ 8.944e+05,  1.073e+06)   |
[ 1.073e+06,  1.252e+06)   |
[ 1.252e+06,  1.431e+06)   |
[ 1.431e+06,  1.610e+06)   |
[ 1.610e+06,  1.789e+06)   |
[ 1.789e+06,  1.968e+06)   |
[ 1.968e+06,  2.147e+06)   |
[ 2.147e+06,  2.326e+06)   |
[ 2.326e+06,  2.504e+06)   |
[ 2.504e+06,  2.683e+06)   |
[ 2.683e+06,  2.862e+06)   |
[ 2.862e+06,  3.041e+06)   |
[ 3.041e+06,  3.220e+06)   |
[ 3.220e+06,  3.399e+06)   |
[ 3.399e+06,  3.578e+06)   |-
[ 3.578e+06,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  39.2          15    Sigma:  +3.26  Odds: 1 in 9.1e+02    Unusual
Neyman's smooth test                        12.1          10    Sigma:  +0.60  Odds: 1 in    1.8    
    Neyman V1: mean                        0.467           0    Sigma:  +0.47  Odds: 1 in    1.6    
    Neyman V2: variance                     1.09           0    Sigma:  +1.09  Odds: 1 in    3.6    
    Neyman V3: skewness                     -1.4           0    Sigma:  -1.40  Odds: 1 in    6.2    
    Neyman V4: kurtosis                    -1.73           0    Sigma:  -1.73  Odds: 1 in    12.    
    Neyman remainder: fine structure         249         251    Sigma:  -0.05  Odds: 1 in    1.0    
Anderson-Darling EDF test                  0.954           1    Sigma:  +0.30  Odds: 1 in    1.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing beta distribution, shape 2, scale 5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.2857	  0.1597	 0.02551	  0.5963	 -0.1200
1.000e+06	  0.2857	  0.1598	 0.02552	  0.5990	 -0.1188
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#############-
[   0.05000,     0.1000)   |#################################-
[    0.1000,     0.1500)   |############################################=
[    0.1500,     0.2000)   |#################################################=
[    0.2000,     0.2500)   |##################################################
[    0.2500,     0.3000)   |##############################################-
[    0.3000,     0.3500)   |#########################################-
[    0.3500,     0.4000)   |###################################-
[    0.4000,     0.4500)   |############################=
[    0.4500,     0.5000)   |######################-
[    0.5000,     0.5500)   |################-
[    0.5500,     0.6000)   |###########=
[    0.6000,     0.6500)   |#######=
[    0.6500,     0.7000)   |####=
[    0.7000,     0.7500)   |##=
[    0.7500,     0.8000)   |#-
[    0.8000,     0.8500)   |-
[    0.8500,     0.9000)   |-
[    0.9000,     0.9500)   |-
[    0.9500,      1.000)   |-
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  19.6          15    Sigma:  +0.88  Odds: 1 in    2.7    
Neyman's smooth test                        12.5          10    Sigma:  +0.66  Odds: 1 in    2.0    
    Neyman V1: mean                       -0.287           0    Sigma:  -0.29  Odds: 1 in    1.3    
    Neyman V2: variance                   -0.266           0    Sigma:  -0.27  Odds: 1 in    1.3    
    Neyman V3: skewness                     2.34           0    Sigma:  +2.34  Odds: 1 in    51.    
    Neyman V4: kurtosis                   -0.214           0    Sigma:  -0.21  Odds: 1 in    1.2    
    Neyman remainder: fine structure         223         251    Sigma:  -1.29  Odds: 1 in    5.0    
Anderson-Darling EDF test                  0.681           1    Sigma:  -0.19  Odds: 1 in    1.2    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing beta distribution, shape 2, scale 5, left 0, right 1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.2857	  0.1597	 0.02551	  0.5963	 -0.1200
1.000e+06	  0.2858	  0.1598	 0.02553	  0.5985	 -0.1133
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#############-
[   0.05000,     0.1000)   |#################################=
[    0.1000,     0.1500)   |############################################=
[    0.1500,     0.2000)   |#################################################=
[    0.2000,     0.2500)   |##################################################
[    0.2500,     0.3000)   |##############################################=
[    0.3000,     0.3500)   |#########################################-
[    0.3500,     0.4000)   |###################################-
[    0.4000,     0.4500)   |############################=
[    0.4500,     0.5000)   |######################-
[    0.5000,     0.5500)   |################=
[    0.5500,     0.6000)   |###########=
[    0.6000,     0.6500)   |#######=
[    0.6500,     0.7000)   |####=
[    0.7000,     0.7500)   |##=
[    0.7500,     0.8000)   |#-
[    0.8000,     0.8500)   |=
[    0.8500,     0.9000)   |-
[    0.9000,     0.9500)   |-
[    0.9500,      1.000)   |-
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  8.41          15    Sigma:  -1.32  Odds: 1 in    5.3    
Neyman's smooth test                        4.29          10    Sigma:  -1.50  Odds: 1 in    7.5    
    Neyman V1: mean                        0.276           0    Sigma:  +0.28  Odds: 1 in    1.3    
    Neyman V2: variance                  -0.0772           0    Sigma:  -0.08  Odds: 1 in    1.1    
    Neyman V3: skewness                    0.768           0    Sigma:  +0.77  Odds: 1 in    2.3    
    Neyman V4: kurtosis                    0.441           0    Sigma:  +0.44  Odds: 1 in    1.5    
    Neyman remainder: fine structure         237         251    Sigma:  -0.60  Odds: 1 in    1.8    
Anderson-Darling EDF test                  0.216           1    Sigma:  -2.18  Odds: 1 in    34.    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +1.89  Odds: 1 in    17.    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing beta distribution, shape 0.5, scale 2, left 0, right 1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.2000	  0.2138	 0.04571	   1.247	  0.8182
1.000e+06	  0.1998	  0.2139	 0.04574	   1.250	  0.8236
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |##################################################
[   0.05000,     0.1000)   |###################-
[    0.1000,     0.1500)   |##############-
[    0.1500,     0.2000)   |###########-
[    0.2000,     0.2500)   |#########-
[    0.2500,     0.3000)   |#######=
[    0.3000,     0.3500)   |######=
[    0.3500,     0.4000)   |#####=
[    0.4000,     0.4500)   |####=
[    0.4500,     0.5000)   |####-
[    0.5000,     0.5500)   |###=
[    0.5500,     0.6000)   |###-
[    0.6000,     0.6500)   |##=
[    0.6500,     0.7000)   |##-
[    0.7000,     0.7500)   |#=
[    0.7500,     0.8000)   |#-
[    0.8000,     0.8500)   |#-
[    0.8500,     0.9000)   |=
[    0.9000,     0.9500)   |-
[    0.9500,      1.000)   |-
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  8.41          15    Sigma:  -1.32  Odds: 1 in    5.3    
Neyman's smooth test                        12.2          10    Sigma:  +0.61  Odds: 1 in    1.8    
    Neyman V1: mean                        -1.35           0    Sigma:  -1.35  Odds: 1 in    5.7    
    Neyman V2: variance                    0.343           0    Sigma:  +0.34  Odds: 1 in    1.4    
    Neyman V3: skewness                    0.976           0    Sigma:  +0.98  Odds: 1 in    3.0    
    Neyman V4: kurtosis                    0.592           0    Sigma:  +0.59  Odds: 1 in    1.8    
    Neyman remainder: fine structure         290         251    Sigma:  +1.67  Odds: 1 in    11.    
Anderson-Darling EDF test                   1.17           1    Sigma:  +0.58  Odds: 1 in    1.8    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing beta distribution, shape 0.5, scale 0.5, left 2, right 5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   3.500	   1.061	   1.125	   0.000	  -1.500
1.000e+06	   3.500	   1.060	   1.124	0.0002042	  -1.499
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      2.200)   |##################################################
[     2.200,      2.400)   |#####################-
[     2.400,      2.600)   |#################-
[     2.600,      2.800)   |###############-
[     2.800,      3.000)   |#############=
[     3.000,      3.200)   |#############-
[     3.200,      3.400)   |############=
[     3.400,      3.600)   |############=
[     3.600,      3.800)   |############=
[     3.800,      4.000)   |#############-
[     4.000,      4.200)   |#############=
[     4.200,      4.400)   |###############-
[     4.400,      4.600)   |#################-
[     4.600,      4.800)   |#####################-
[     4.800,      5.000)   |#################################################=
[     5.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  11.9          15    Sigma:  -0.48  Odds: 1 in    1.6    
Neyman's smooth test                        8.98          10    Sigma:  -0.08  Odds: 1 in    1.1    
    Neyman V1: mean                      -0.0909           0    Sigma:  -0.09  Odds: 1 in    1.1    
    Neyman V2: variance                   -0.159           0    Sigma:  -0.16  Odds: 1 in    1.1    
    Neyman V3: skewness                    0.398           0    Sigma:  +0.40  Odds: 1 in    1.4    
    Neyman V4: kurtosis                     2.22           0    Sigma:  +2.22  Odds: 1 in    38.    
    Neyman remainder: fine structure         244         251    Sigma:  -0.31  Odds: 1 in    1.3    
Anderson-Darling EDF test                  0.425           1    Sigma:  -0.93  Odds: 1 in    2.8    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.38  Odds: 1 in    1.4    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing beta distribution, shape 0.5, scale 0.5, left -2, right 2
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   0.000	   1.414	   2.000	   0.000	  -1.500
1.000e+06	-0.0005428	   1.414	   1.998	0.0007923	  -1.499
--------------------------------------------------------------------------------
( -Infinity,     -2.000)   |
[    -2.000,     -1.800)   |#################################################=
[    -1.800,     -1.600)   |#####################-
[    -1.600,     -1.400)   |################=
[    -1.400,     -1.200)   |##############=
[    -1.200,     -1.000)   |#############-
[    -1.000,    -0.8000)   |############-
[   -0.8000,    -0.6000)   |###########=
[   -0.6000,    -0.4000)   |###########=
[   -0.4000,    -0.2000)   |###########-
[   -0.2000,      0.000)   |###########-
[     0.000,     0.2000)   |###########-
[    0.2000,     0.4000)   |###########-
[    0.4000,     0.6000)   |###########-
[    0.6000,     0.8000)   |############-
[    0.8000,      1.000)   |############=
[     1.000,      1.200)   |#############-
[     1.200,      1.400)   |##############=
[     1.400,      1.600)   |################=
[     1.600,      1.800)   |#####################-
[     1.800,      2.000)   |##################################################
[     2.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  6.71          15    Sigma:  -1.81  Odds: 1 in    14.    
Neyman's smooth test                        5.97          10    Sigma:  -0.91  Odds: 1 in    2.7    
    Neyman V1: mean                        -0.28           0    Sigma:  -0.28  Odds: 1 in    1.3    
    Neyman V2: variance                    -1.05           0    Sigma:  -1.05  Odds: 1 in    3.4    
    Neyman V3: skewness                    0.918           0    Sigma:  +0.92  Odds: 1 in    2.8    
    Neyman V4: kurtosis                    0.415           0    Sigma:  +0.41  Odds: 1 in    1.5    
    Neyman remainder: fine structure         248         251    Sigma:  -0.11  Odds: 1 in    1.1    
Anderson-Darling EDF test                  0.428           1    Sigma:  -0.92  Odds: 1 in    2.8    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.36  Odds: 1 in    1.4    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing PERT distribution, left 2, mode 5, right 10
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   5.333	   1.491	   2.222	  0.2236	 -0.6000
1.000e+06	   5.334	   1.491	   2.223	  0.2238	 -0.5985
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      2.500)   |###=
[     2.500,      3.000)   |################-
[     3.000,      3.500)   |############################=
[     3.500,      4.000)   |#######################################-
[     4.000,      4.500)   |##############################################-
[     4.500,      5.000)   |##################################################
[     5.000,      5.500)   |#################################################=
[     5.500,      6.000)   |##############################################=
[     6.000,      6.500)   |#########################################-
[     6.500,      7.000)   |##################################-
[     7.000,      7.500)   |##########################-
[     7.500,      8.000)   |##################-
[     8.000,      8.500)   |###########-
[     8.500,      9.000)   |#####-
[     9.000,      9.500)   |#=
[     9.500,      10.00)   |-
[     10.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                    11          15    Sigma:  -0.67  Odds: 1 in    2.0    
Neyman's smooth test                        3.54          10    Sigma:  -1.82  Odds: 1 in    15.    
    Neyman V1: mean                          0.2           0    Sigma:  +0.20  Odds: 1 in    1.2    
    Neyman V2: variance                   -0.148           0    Sigma:  -0.15  Odds: 1 in    1.1    
    Neyman V3: skewness                    0.315           0    Sigma:  +0.31  Odds: 1 in    1.3    
    Neyman V4: kurtosis                    0.862           0    Sigma:  +0.86  Odds: 1 in    2.6    
    Neyman remainder: fine structure         244         251    Sigma:  -0.28  Odds: 1 in    1.3    
Anderson-Darling EDF test                  0.275           1    Sigma:  -1.70  Odds: 1 in    11.    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +1.49  Odds: 1 in    7.3    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing modified PERT distribution, left 2, mode 5, right 10, lambda 5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   5.286	   1.391	   1.936	  0.2281	 -0.5297
1.000e+06	   5.286	   1.391	   1.935	  0.2277	 -0.5264
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      2.500)   |##-
[     2.500,      3.000)   |############-
[     3.000,      3.500)   |########################=
[     3.500,      4.000)   |####################################=
[     4.000,      4.500)   |#############################################-
[     4.500,      5.000)   |#################################################=
[     5.000,      5.500)   |##################################################
[     5.500,      6.000)   |##############################################-
[     6.000,      6.500)   |#######################################-
[     6.500,      7.000)   |##############################=
[     7.000,      7.500)   |######################-
[     7.500,      8.000)   |##############-
[     8.000,      8.500)   |#######=
[     8.500,      9.000)   |###-
[     9.000,      9.500)   |=
[     9.500,      10.00)   |-
[     10.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  13.9          15    Sigma:  -0.08  Odds: 1 in    1.1    
Neyman's smooth test                        12.3          10    Sigma:  +0.62  Odds: 1 in    1.9    
    Neyman V1: mean                        0.396           0    Sigma:  +0.40  Odds: 1 in    1.4    
    Neyman V2: variance                    -1.08           0    Sigma:  -1.08  Odds: 1 in    3.6    
    Neyman V3: skewness                   -0.401           0    Sigma:  -0.40  Odds: 1 in    1.5    
    Neyman V4: kurtosis                     1.17           0    Sigma:  +1.17  Odds: 1 in    4.1    
    Neyman remainder: fine structure         294         251    Sigma:  +1.83  Odds: 1 in    15.    
Anderson-Darling EDF test                   0.53           1    Sigma:  -0.57  Odds: 1 in    1.8    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing modified PERT distribution, left 2, mode 3, right 5, lambda 2
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   3.250	  0.6614	  0.4375	  0.2520	 -0.7755
1.000e+06	   3.250	  0.6621	  0.4384	  0.2538	 -0.7740
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      2.200)   |################=
[     2.200,      2.400)   |#################################-
[     2.400,      2.600)   |##########################################=
[     2.600,      2.800)   |###############################################=
[     2.800,      3.000)   |##################################################
[     3.000,      3.200)   |#################################################=
[     3.200,      3.400)   |################################################-
[     3.400,      3.600)   |############################################=
[     3.600,      3.800)   |########################################-
[     3.800,      4.000)   |##################################=
[     4.000,      4.200)   |############################-
[     4.200,      4.400)   |#####################=
[     4.400,      4.600)   |##############=
[     4.600,      4.800)   |#######=
[     4.800,      5.000)   |##-
[     5.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  14.4          15    Sigma:  +0.00  Odds: 1 in    1.0    
Neyman's smooth test                        6.33          10    Sigma:  -0.80  Odds: 1 in    2.3    
    Neyman V1: mean                       -0.153           0    Sigma:  -0.15  Odds: 1 in    1.1    
    Neyman V2: variance                     1.32           0    Sigma:  +1.32  Odds: 1 in    5.4    
    Neyman V3: skewness                    0.614           0    Sigma:  +0.61  Odds: 1 in    1.9    
    Neyman V4: kurtosis                     0.57           0    Sigma:  +0.57  Odds: 1 in    1.8    
    Neyman remainder: fine structure         255         251    Sigma:  +0.20  Odds: 1 in    1.2    
Anderson-Darling EDF test                  0.637           1    Sigma:  -0.29  Odds: 1 in    1.3    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.19  Odds: 1 in    1.2    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Pareto distribution, shape 3, scale 2
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   3.000	   1.732	   3.000	   ---  	   ---  
1.000e+06	   2.999	   1.681	   2.826	   11.04	   392.9
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      9.000)   |##################################################
[     9.000,      18.00)   |-
[     18.00,      27.00)   |-
[     27.00,      36.00)   |-
[     36.00,      45.00)   |-
[     45.00,      54.00)   |-
[     54.00,      63.00)   |-
[     63.00,      72.00)   |-
[     72.00,      81.00)   |-
[     81.00,      90.00)   |-
[     90.00,      99.00)   |-
[     99.00,      108.0)   |-
[     108.0,      117.0)   |-
[     117.0,      126.0)   |
[     126.0,      135.0)   |
[     135.0,      144.0)   |
[     144.0,      153.0)   |
[     153.0,      162.0)   |
[     162.0,      171.0)   |
[     171.0,      180.0)   |-
[     180.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  15.5          15    Sigma:  +0.22  Odds: 1 in    1.2    
Neyman's smooth test                        10.3          10    Sigma:  +0.21  Odds: 1 in    1.2    
    Neyman V1: mean                        0.481           0    Sigma:  +0.48  Odds: 1 in    1.6    
    Neyman V2: variance                   -0.896           0    Sigma:  -0.90  Odds: 1 in    2.7    
    Neyman V3: skewness                    0.973           0    Sigma:  +0.97  Odds: 1 in    3.0    
    Neyman V4: kurtosis                    -1.37           0    Sigma:  -1.37  Odds: 1 in    5.9    
    Neyman remainder: fine structure         268         251    Sigma:  +0.76  Odds: 1 in    2.2    
Anderson-Darling EDF test                  0.696           1    Sigma:  -0.16  Odds: 1 in    1.1    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing chisquare distribution, v 4
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   4.000	   2.828	   8.000	   1.414	   3.000
1.000e+06	   3.997	   2.822	   7.964	   1.408	   2.986
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |########################################-
[     2.000,      4.000)   |##################################################
[     4.000,      6.000)   |###############################-
[     6.000,      8.000)   |################-
[     8.000,      10.00)   |#######=
[     10.00,      12.00)   |###-
[     12.00,      14.00)   |#=
[     14.00,      16.00)   |=
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |-
[     28.00,      30.00)   |-
[     30.00,      32.00)   |-
[     32.00,      34.00)   |-
[     34.00,      36.00)   |-
[     36.00,      38.00)   |-
[     38.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  17.1          15    Sigma:  +0.48  Odds: 1 in    1.6    
Neyman's smooth test                        10.4          10    Sigma:  +0.23  Odds: 1 in    1.2    
    Neyman V1: mean                       -0.416           0    Sigma:  -0.42  Odds: 1 in    1.5    
    Neyman V2: variance                   -0.941           0    Sigma:  -0.94  Odds: 1 in    2.9    
    Neyman V3: skewness                    -1.74           0    Sigma:  -1.74  Odds: 1 in    12.    
    Neyman V4: kurtosis                    0.637           0    Sigma:  +0.64  Odds: 1 in    1.9    
    Neyman remainder: fine structure         264         251    Sigma:  +0.59  Odds: 1 in    1.8    
Anderson-Darling EDF test                  0.811           1    Sigma:  +0.07  Odds: 1 in    1.1    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing f distribution, a 3, b 5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.667	   3.333	   11.11	   ---  	   ---  
1.000e+06	   1.665	   3.034	   9.207	   23.48	   2230.
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      27.00)   |##################################################
[     27.00,      54.00)   |-
[     54.00,      81.00)   |-
[     81.00,      108.0)   |-
[     108.0,      135.0)   |-
[     135.0,      162.0)   |-
[     162.0,      189.0)   |-
[     189.0,      216.0)   |-
[     216.0,      243.0)   |-
[     243.0,      270.0)   |
[     270.0,      297.0)   |-
[     297.0,      324.0)   |
[     324.0,      351.0)   |
[     351.0,      378.0)   |-
[     378.0,      405.0)   |
[     405.0,      432.0)   |
[     432.0,      459.0)   |
[     459.0,      486.0)   |-
[     486.0,      513.0)   |
[     513.0,      540.0)   |-
[     540.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  17.7          15    Sigma:  +0.58  Odds: 1 in    1.8    
Neyman's smooth test                        9.81          10    Sigma:  +0.11  Odds: 1 in    1.1    
    Neyman V1: mean                       0.0134           0    Sigma:  +0.01  Odds: 1 in    1.0    
    Neyman V2: variance                      1.9           0    Sigma:  +1.90  Odds: 1 in    17.    
    Neyman V3: skewness                   -0.171           0    Sigma:  -0.17  Odds: 1 in    1.2    
    Neyman V4: kurtosis                    -1.39           0    Sigma:  -1.39  Odds: 1 in    6.0    
    Neyman remainder: fine structure         248         251    Sigma:  -0.12  Odds: 1 in    1.1    
Anderson-Darling EDF test                  0.872           1    Sigma:  +0.17  Odds: 1 in    1.2    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Student's t distribution, v 3
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   0.000	   1.732	   3.000	   ---  	   ---  
1.000e+06	0.002070	   1.749	   3.058	 -0.9986	   317.6
--------------------------------------------------------------------------------
( -Infinity,     -198.0)   |
[    -198.0,     -180.0)   |-
[    -180.0,     -162.0)   |
[    -162.0,     -144.0)   |
[    -144.0,     -126.0)   |
[    -126.0,     -108.0)   |
[    -108.0,     -90.00)   |-
[    -90.00,     -72.00)   |-
[    -72.00,     -54.00)   |-
[    -54.00,     -36.00)   |-
[    -36.00,     -18.00)   |-
[    -18.00,      0.000)   |#################################################=
[     0.000,      18.00)   |##################################################
[     18.00,      36.00)   |-
[     36.00,      54.00)   |-
[     54.00,      72.00)   |-
[     72.00,      90.00)   |-
[     90.00,      108.0)   |-
[     108.0,      126.0)   |
[     126.0,      144.0)   |
[     144.0,      162.0)   |-
[     162.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  12.5          15    Sigma:  -0.36  Odds: 1 in    1.4    
Neyman's smooth test                        19.3          10    Sigma:  +1.80  Odds: 1 in    14.    
    Neyman V1: mean                         1.36           0    Sigma:  +1.36  Odds: 1 in    5.7    
    Neyman V2: variance                     1.08           0    Sigma:  +1.08  Odds: 1 in    3.6    
    Neyman V3: skewness                    0.595           0    Sigma:  +0.60  Odds: 1 in    1.8    
    Neyman V4: kurtosis                    0.875           0    Sigma:  +0.87  Odds: 1 in    2.6    
    Neyman remainder: fine structure         317         251    Sigma:  +2.74  Odds: 1 in 1.6e+02    
Anderson-Darling EDF test                   1.37           1    Sigma:  +0.80  Odds: 1 in    2.4    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +1.46  Odds: 1 in    6.9    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing t distribution, m 1, s 2, v 3,
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.000	   3.464	   12.00	   ---  	   ---  
1.000e+06	   1.001	   3.430	   11.77	 -0.2467	   82.59
--------------------------------------------------------------------------------
( -Infinity,     -252.0)   |
[    -252.0,     -231.0)   |-
[    -231.0,     -210.0)   |
[    -210.0,     -189.0)   |
[    -189.0,     -168.0)   |
[    -168.0,     -147.0)   |
[    -147.0,     -126.0)   |-
[    -126.0,     -105.0)   |-
[    -105.0,     -84.00)   |-
[    -84.00,     -63.00)   |-
[    -63.00,     -42.00)   |-
[    -42.00,     -21.00)   |-
[    -21.00,      0.000)   |########################-
[     0.000,      21.00)   |##################################################
[     21.00,      42.00)   |-
[     42.00,      63.00)   |-
[     63.00,      84.00)   |-
[     84.00,      105.0)   |-
[     105.0,      126.0)   |-
[     126.0,      147.0)   |-
[     147.0,      168.0)   |-
[     168.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  21.7          15    Sigma:  +1.20  Odds: 1 in    4.3    
Neyman's smooth test                        14.6          10    Sigma:  +1.05  Odds: 1 in    3.4    
    Neyman V1: mean                        0.547           0    Sigma:  +0.55  Odds: 1 in    1.7    
    Neyman V2: variance                    0.587           0    Sigma:  +0.59  Odds: 1 in    1.8    
    Neyman V3: skewness                     -1.2           0    Sigma:  -1.20  Odds: 1 in    4.3    
    Neyman V4: kurtosis                     2.48           0    Sigma:  +2.48  Odds: 1 in    77.    
    Neyman remainder: fine structure         260         251    Sigma:  +0.41  Odds: 1 in    1.5    
Anderson-Darling EDF test                   0.83           1    Sigma:  +0.10  Odds: 1 in    1.1    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  +0.54  Odds: 1 in    1.7    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Rayleigh distribution, s 1.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.880	  0.9827	  0.9657	  0.6311	  0.2451
1.000e+06	   1.879	  0.9822	  0.9647	  0.6339	  0.2622
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |#############=
[    0.5000,      1.000)   |#####################################-
[     1.000,      1.500)   |##################################################
[     1.500,      2.000)   |##################################################
[     2.000,      2.500)   |#########################################=
[     2.500,      3.000)   |#############################-
[     3.000,      3.500)   |#################=
[     3.500,      4.000)   |#########=
[     4.000,      4.500)   |####-
[     4.500,      5.000)   |#=
[     5.000,      5.500)   |=
[     5.500,      6.000)   |-
[     6.000,      6.500)   |-
[     6.500,      7.000)   |-
[     7.000,      7.500)   |-
[     7.500,      8.000)   |-
[     8.000,      8.500)   |-
[     8.500,      9.000)   |-
[     9.000,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  8.27          15    Sigma:  -1.36  Odds: 1 in    5.7    
Neyman's smooth test                        7.51          10    Sigma:  -0.46  Odds: 1 in    1.5    
    Neyman V1: mean                       -0.789           0    Sigma:  -0.79  Odds: 1 in    2.3    
    Neyman V2: variance                    -1.04           0    Sigma:  -1.04  Odds: 1 in    3.4    
    Neyman V3: skewness                   -0.465           0    Sigma:  -0.46  Odds: 1 in    1.6    
    Neyman V4: kurtosis                   0.0823           0    Sigma:  +0.08  Odds: 1 in    1.1    
    Neyman remainder: fine structure         228         251    Sigma:  -1.02  Odds: 1 in    3.3    
Anderson-Darling EDF test                  0.653           1    Sigma:  -0.25  Odds: 1 in    1.2    
Combined assessment, Bonferroni on Neyman + Anderson-Darling:   Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------
************************* Integer-valued distributions *************************

Quality testing unbiased coin flip, p = 0.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.5000	  0.5000	  0.2500	   0.000	  -2.000
1.000e+06	  0.5003	  0.5000	  0.2500	-0.001344	  -2.000
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#################################################=
[   0.05000,     0.1000)   |
[    0.1000,     0.1500)   |
[    0.1500,     0.2000)   |
[    0.2000,     0.2500)   |
[    0.2500,     0.3000)   |
[    0.3000,     0.3500)   |
[    0.3500,     0.4000)   |
[    0.4000,     0.4500)   |
[    0.4500,     0.5000)   |
[    0.5000,     0.5500)   |
[    0.5500,     0.6000)   |
[    0.6000,     0.6500)   |
[    0.6500,     0.7000)   |
[    0.7000,     0.7500)   |
[    0.7500,     0.8000)   |
[    0.8000,     0.8500)   |
[    0.8500,     0.9000)   |
[    0.9000,     0.9500)   |
[    0.9500,      1.000)   |
[     1.000,      1.050)   |##################################################
[     1.050,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                 0.452           1    Sigma:  -0.00  Odds: 1 in    1.0    
Combined assessment (Pearson only due to few discrete values):  Sigma:  -0.00  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing biased Bernoulli trials, p = 0.1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.1000	  0.3000	 0.09000	   2.667	   5.111
1.000e+06	 0.09978	  0.2997	 0.08982	   2.671	   5.133
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |##################################################-
[   0.05000,     0.1000)   |
[    0.1000,     0.1500)   |
[    0.1500,     0.2000)   |
[    0.2000,     0.2500)   |
[    0.2500,     0.3000)   |
[    0.3000,     0.3500)   |
[    0.3500,     0.4000)   |
[    0.4000,     0.4500)   |
[    0.4500,     0.5000)   |
[    0.5000,     0.5500)   |
[    0.5500,     0.6000)   |
[    0.6000,     0.6500)   |
[    0.6500,     0.7000)   |
[    0.7000,     0.7500)   |
[    0.7500,     0.8000)   |
[    0.8000,     0.8500)   |
[    0.8500,     0.9000)   |
[    0.9000,     0.9500)   |
[    0.9500,      1.000)   |
[     1.000,      1.050)   |#####=
[     1.050,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                 0.543           1    Sigma:  +0.10  Odds: 1 in    1.1    
Combined assessment (Pearson only due to few discrete values):  Sigma:  +0.10  Odds: 1 in    1.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing biased Bernoulli trials, p = 0.6
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	  0.6000	  0.4899	  0.2400	 -0.4082	  -1.833
1.000e+06	  0.6002	  0.4899	  0.2400	 -0.4090	  -1.833
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#################################-
[   0.05000,     0.1000)   |
[    0.1000,     0.1500)   |
[    0.1500,     0.2000)   |
[    0.2000,     0.2500)   |
[    0.2500,     0.3000)   |
[    0.3000,     0.3500)   |
[    0.3500,     0.4000)   |
[    0.4000,     0.4500)   |
[    0.4500,     0.5000)   |
[    0.5000,     0.5500)   |
[    0.5500,     0.6000)   |
[    0.6000,     0.6500)   |
[    0.6500,     0.7000)   |
[    0.7000,     0.7500)   |
[    0.7500,     0.8000)   |
[    0.8000,     0.8500)   |
[    0.8500,     0.9000)   |
[    0.9000,     0.9500)   |
[    0.9500,      1.000)   |
[     1.000,      1.050)   |##################################################
[     1.050,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                 0.132           1    Sigma:  -0.57  Odds: 1 in    1.8    
Combined assessment (Pearson only due to few discrete values):  Sigma:  -0.57  Odds: 1 in    1.8    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing geometric distribution, p = 0.1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   10.00	   9.487	   90.00	   2.003	   6.011
1.000e+06	   9.996	   9.492	   90.09	   2.006	   5.963
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      7.000)   |##################################################
[     7.000,      14.00)   |#############################=
[     14.00,      21.00)   |##############-
[     21.00,      28.00)   |######=
[     28.00,      35.00)   |###-
[     35.00,      42.00)   |#=
[     42.00,      49.00)   |=
[     49.00,      56.00)   |-
[     56.00,      63.00)   |-
[     63.00,      70.00)   |-
[     70.00,      77.00)   |-
[     77.00,      84.00)   |-
[     84.00,      91.00)   |-
[     91.00,      98.00)   |-
[     98.00,      105.0)   |-
[     105.0,      112.0)   |-
[     112.0,      119.0)   |-
[     119.0,      126.0)   |
[     126.0,      133.0)   |
[     133.0,      140.0)   |-
[     140.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  11.7          20    Sigma:  -1.45  Odds: 1 in    6.8    
Neyman's smooth test                        8.07          10    Sigma:  -0.31  Odds: 1 in    1.3    
    Neyman V1: mean                       -0.827           0    Sigma:  -0.83  Odds: 1 in    2.4    
    Neyman V2: variance                    -0.65           0    Sigma:  -0.65  Odds: 1 in    1.9    
    Neyman V3: skewness                    0.651           0    Sigma:  +0.65  Odds: 1 in    1.9    
    Neyman V4: kurtosis                   -0.483           0    Sigma:  -0.48  Odds: 1 in    1.6    
    Neyman remainder: fine structure        9.93          16    Sigma:  -1.13  Odds: 1 in    3.9    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.31  Odds: 1 in    1.3    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing geometric distribution, p = 0.6
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.667	   1.054	   1.111	   2.214	   6.900
1.000e+06	   1.665	   1.053	   1.108	   2.231	   7.121
--------------------------------------------------------------------------------
( -Infinity,      1.000)   |
[     1.000,      2.000)   |##################################################
[     2.000,      3.000)   |####################-
[     3.000,      4.000)   |#######=
[     4.000,      5.000)   |###-
[     5.000,      6.000)   |#-
[     6.000,      7.000)   |=
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |-
[     13.00,      14.00)   |-
[     14.00,      15.00)   |-
[     15.00,      16.00)   |-
[     16.00,      17.00)   |-
[     17.00,      18.00)   |
[     18.00,      19.00)   |
[     19.00,      20.00)   |-
[     20.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  17.3          12    Sigma:  +1.09  Odds: 1 in    3.6    
Neyman's smooth test                        13.8          10    Sigma:  +0.90  Odds: 1 in    2.7    
    Neyman V1: mean                         1.65           0    Sigma:  +1.65  Odds: 1 in    10.    
    Neyman V2: variance                    0.479           0    Sigma:  +0.48  Odds: 1 in    1.6    
    Neyman V3: skewness                      2.2           0    Sigma:  +2.20  Odds: 1 in    36.    
    Neyman V4: kurtosis                   -0.031           0    Sigma:  -0.03  Odds: 1 in    1.0    
    Neyman remainder: fine structure        9.53           8    Sigma:  +0.53  Odds: 1 in    1.7    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +0.90  Odds: 1 in    2.7    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing binomial distribution, n = 10, p = 0.1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   1.000	  0.9487	  0.9000	  0.8433	  0.5111
1.000e+06	   1.001	  0.9487	  0.9001	  0.8441	  0.5165
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |############################################=
[    0.5000,      1.000)   |
[     1.000,      1.500)   |##################################################
[     1.500,      2.000)   |
[     2.000,      2.500)   |########################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |#######-
[     3.500,      4.000)   |
[     4.000,      4.500)   |#-
[     4.500,      5.000)   |
[     5.000,      5.500)   |-
[     5.500,      6.000)   |
[     6.000,      6.500)   |-
[     6.500,      7.000)   |
[     7.000,      7.500)   |-
[     7.500,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  4.81           6    Sigma:  -0.17  Odds: 1 in    1.2    
Neyman's smooth test                        7.05          10    Sigma:  -0.58  Odds: 1 in    1.8    
    Neyman V1: mean                        0.741           0    Sigma:  +0.74  Odds: 1 in    2.2    
    Neyman V2: variance                   -0.416           0    Sigma:  -0.42  Odds: 1 in    1.5    
    Neyman V3: skewness                    0.961           0    Sigma:  +0.96  Odds: 1 in    3.0    
    Neyman V4: kurtosis                   -0.535           0    Sigma:  -0.54  Odds: 1 in    1.7    
    Neyman remainder: fine structure        2.88           2    Sigma:  +0.71  Odds: 1 in    2.1    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.58  Odds: 1 in    1.8    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing binomial distribution, n = 100, p = 0.5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   50.00	   5.000	   25.00	   0.000	-0.02000
1.000e+06	   50.00	   4.998	   24.98	0.0007127	-0.01963
--------------------------------------------------------------------------------
( -Infinity,      21.00)   |
[     21.00,      24.00)   |-
[     24.00,      27.00)   |-
[     27.00,      30.00)   |-
[     30.00,      33.00)   |-
[     33.00,      36.00)   |-
[     36.00,      39.00)   |#=
[     39.00,      42.00)   |#######-
[     42.00,      45.00)   |###################=
[     45.00,      48.00)   |#####################################-
[     48.00,      51.00)   |##################################################
[     51.00,      54.00)   |###############################################-
[     54.00,      57.00)   |###############################-
[     57.00,      60.00)   |##############=
[     60.00,      63.00)   |####=
[     63.00,      66.00)   |#-
[     66.00,      69.00)   |-
[     69.00,      72.00)   |-
[     72.00,      75.00)   |-
[     75.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  29.1          42    Sigma:  -1.51  Odds: 1 in    7.6    
Neyman's smooth test                        4.45          10    Sigma:  -1.44  Odds: 1 in    6.6    
    Neyman V1: mean                        0.129           0    Sigma:  +0.13  Odds: 1 in    1.1    
    Neyman V2: variance                   -0.509           0    Sigma:  -0.51  Odds: 1 in    1.6    
    Neyman V3: skewness                    0.327           0    Sigma:  +0.33  Odds: 1 in    1.3    
    Neyman V4: kurtosis                  -0.0564           0    Sigma:  -0.06  Odds: 1 in    1.0    
    Neyman remainder: fine structure        28.7          38    Sigma:  -1.08  Odds: 1 in    3.6    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -1.44  Odds: 1 in    6.6    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing binomial distribution, n = 50, p = 0.7
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   35.00	   3.240	   10.50	 -0.1234	-0.02476
1.000e+06	   35.00	   3.241	   10.50	 -0.1246	-0.02544
--------------------------------------------------------------------------------
( -Infinity,      18.00)   |
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |##-
[     28.00,      30.00)   |#######-
[     30.00,      32.00)   |###################=
[     32.00,      34.00)   |####################################=
[     34.00,      36.00)   |##################################################
[     36.00,      38.00)   |###############################################-
[     38.00,      40.00)   |##############################-
[     40.00,      42.00)   |############=
[     42.00,      44.00)   |###-
[     44.00,      46.00)   |-
[     46.00,      48.00)   |-
[     48.00,      50.00)   |-
[     50.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                    17          27    Sigma:  -1.48  Odds: 1 in    7.2    
Neyman's smooth test                        5.93          10    Sigma:  -0.92  Odds: 1 in    2.8    
    Neyman V1: mean                       -0.834           0    Sigma:  -0.83  Odds: 1 in    2.5    
    Neyman V2: variance                   0.0965           0    Sigma:  +0.10  Odds: 1 in    1.1    
    Neyman V3: skewness                   -0.484           0    Sigma:  -0.48  Odds: 1 in    1.6    
    Neyman V4: kurtosis                     -0.3           0    Sigma:  -0.30  Odds: 1 in    1.3    
    Neyman remainder: fine structure          16          23    Sigma:  -1.06  Odds: 1 in    3.5    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.92  Odds: 1 in    2.8    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing negative binomial (Pascal) distribution, m = 10, p = 0.1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   90.00	   30.00	   900.0	  0.6333	  0.6011
1.000e+06	   90.03	   29.99	   899.6	  0.6366	  0.6200
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      16.00)   |-
[     16.00,      32.00)   |#-
[     32.00,      48.00)   |###########-
[     48.00,      64.00)   |###############################=
[     64.00,      80.00)   |################################################-
[     80.00,      96.00)   |##################################################
[     96.00,      112.0)   |#######################################-
[     112.0,      128.0)   |#########################-
[     128.0,      144.0)   |##############-
[     144.0,      160.0)   |######=
[     160.0,      176.0)   |###-
[     176.0,      192.0)   |#-
[     192.0,      208.0)   |=
[     208.0,      224.0)   |-
[     224.0,      240.0)   |-
[     240.0,      256.0)   |-
[     256.0,      272.0)   |-
[     272.0,      288.0)   |-
[     288.0,      304.0)   |-
[     304.0,      320.0)   |
[     320.0,      336.0)   |-
[     336.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                   233         237    Sigma:  -0.16  Odds: 1 in    1.1    
Neyman's smooth test                        9.41          10    Sigma:  +0.02  Odds: 1 in    1.0    
    Neyman V1: mean                         0.85           0    Sigma:  +0.85  Odds: 1 in    2.5    
    Neyman V2: variance                   -0.669           0    Sigma:  -0.67  Odds: 1 in    2.0    
    Neyman V3: skewness                     1.48           0    Sigma:  +1.48  Odds: 1 in    7.3    
    Neyman V4: kurtosis                    0.875           0    Sigma:  +0.88  Odds: 1 in    2.6    
    Neyman remainder: fine structure         229         233    Sigma:  -0.17  Odds: 1 in    1.2    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +0.02  Odds: 1 in    1.0    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing negative binomial (Pascal) distribution, m = 50, p = 0.7
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   21.43	   5.533	   30.61	  0.3357	  0.1527
1.000e+06	   21.42	   5.532	   30.60	  0.3387	  0.1545
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      3.000)   |-
[     3.000,      6.000)   |-
[     6.000,      9.000)   |=
[     9.000,      12.00)   |#####-
[     12.00,      15.00)   |#################-
[     15.00,      18.00)   |###################################=
[     18.00,      21.00)   |#################################################=
[     21.00,      24.00)   |##################################################
[     24.00,      27.00)   |######################################-
[     27.00,      30.00)   |#######################-
[     30.00,      33.00)   |###########=
[     33.00,      36.00)   |####=
[     36.00,      39.00)   |#=
[     39.00,      42.00)   |=
[     42.00,      45.00)   |-
[     45.00,      48.00)   |-
[     48.00,      51.00)   |-
[     51.00,      54.00)   |
[     54.00,      57.00)   |-
[     57.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  58.2          47    Sigma:  +1.15  Odds: 1 in    4.0    
Neyman's smooth test                        11.8          10    Sigma:  +0.53  Odds: 1 in    1.7    
    Neyman V1: mean                        -1.52           0    Sigma:  -1.52  Odds: 1 in    7.7    
    Neyman V2: variance                    0.174           0    Sigma:  +0.17  Odds: 1 in    1.2    
    Neyman V3: skewness                     1.15           0    Sigma:  +1.15  Odds: 1 in    4.0    
    Neyman V4: kurtosis                   -0.853           0    Sigma:  -0.85  Odds: 1 in    2.5    
    Neyman remainder: fine structure        53.9          43    Sigma:  +1.16  Odds: 1 in    4.0    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +0.53  Odds: 1 in    1.7    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing negative binomial (Pascal) distribution, m = 1, p = 0.1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   9.000	   9.487	   90.00	   2.003	   6.011
1.000e+06	   9.006	   9.474	   89.75	   1.991	   5.917
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      7.000)   |##################################################
[     7.000,      14.00)   |#######################=
[     14.00,      21.00)   |###########-
[     21.00,      28.00)   |#####=
[     28.00,      35.00)   |##=
[     35.00,      42.00)   |#-
[     42.00,      49.00)   |=
[     49.00,      56.00)   |-
[     56.00,      63.00)   |-
[     63.00,      70.00)   |-
[     70.00,      77.00)   |-
[     77.00,      84.00)   |-
[     84.00,      91.00)   |-
[     91.00,      98.00)   |-
[     98.00,      105.0)   |-
[     105.0,      112.0)   |-
[     112.0,      119.0)   |-
[     119.0,      126.0)   |-
[     126.0,      133.0)   |-
[     133.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  97.4          94    Sigma:  +0.29  Odds: 1 in    1.3    
Neyman's smooth test                        8.22          10    Sigma:  -0.27  Odds: 1 in    1.3    
    Neyman V1: mean                        0.598           0    Sigma:  +0.60  Odds: 1 in    1.8    
    Neyman V2: variance                    -1.99           0    Sigma:  -1.99  Odds: 1 in    22.    
    Neyman V3: skewness                   0.0644           0    Sigma:  +0.06  Odds: 1 in    1.1    
    Neyman V4: kurtosis                    0.169           0    Sigma:  +0.17  Odds: 1 in    1.2    
    Neyman remainder: fine structure          93          90    Sigma:  +0.27  Odds: 1 in    1.3    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.27  Odds: 1 in    1.3    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Poisson distribution, rate = 5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   5.000	   2.236	   5.000	  0.4472	  0.2000
1.000e+06	   4.998	   2.237	   5.006	  0.4501	  0.2015
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |#=
[     1.000,      2.000)   |#########=
[     2.000,      3.000)   |########################-
[     3.000,      4.000)   |########################################-
[     4.000,      5.000)   |#################################################=
[     5.000,      6.000)   |##################################################
[     6.000,      7.000)   |#########################################=
[     7.000,      8.000)   |#############################=
[     8.000,      9.000)   |##################=
[     9.000,      10.00)   |##########-
[     10.00,      11.00)   |#####-
[     11.00,      12.00)   |##-
[     12.00,      13.00)   |=
[     13.00,      14.00)   |-
[     14.00,      15.00)   |-
[     15.00,      16.00)   |-
[     16.00,      17.00)   |-
[     17.00,      18.00)   |-
[     18.00,      19.00)   |-
[     19.00,      20.00)   |
[     20.00,      21.00)   |-
[     21.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  15.1          17    Sigma:  -0.23  Odds: 1 in    1.2    
Neyman's smooth test                        9.08          10    Sigma:  -0.06  Odds: 1 in    1.1    
    Neyman V1: mean                        -1.03           0    Sigma:  -1.03  Odds: 1 in    3.3    
    Neyman V2: variance                     1.12           0    Sigma:  +1.12  Odds: 1 in    3.8    
    Neyman V3: skewness                    0.708           0    Sigma:  +0.71  Odds: 1 in    2.1    
    Neyman V4: kurtosis                   -0.958           0    Sigma:  -0.96  Odds: 1 in    3.0    
    Neyman remainder: fine structure        11.3          13    Sigma:  -0.21  Odds: 1 in    1.2    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.06  Odds: 1 in    1.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Poisson distribution, rate = 16.9
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   16.90	   4.111	   16.90	  0.2433	 0.05917
1.000e+06	   16.90	   4.107	   16.87	  0.2406	 0.04377
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |-
[     2.000,      4.000)   |-
[     4.000,      6.000)   |-
[     6.000,      8.000)   |#-
[     8.000,      10.00)   |#####=
[     10.00,      12.00)   |###############=
[     12.00,      14.00)   |###############################-
[     14.00,      16.00)   |############################################=
[     16.00,      18.00)   |##################################################
[     18.00,      20.00)   |############################################-
[     20.00,      22.00)   |###############################=
[     22.00,      24.00)   |##################=
[     24.00,      26.00)   |#########=
[     26.00,      28.00)   |####-
[     28.00,      30.00)   |#-
[     30.00,      32.00)   |-
[     32.00,      34.00)   |-
[     34.00,      36.00)   |-
[     36.00,      38.00)   |-
[     38.00,      40.00)   |-
[     40.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  32.7          34    Sigma:  -0.07  Odds: 1 in    1.1    
Neyman's smooth test                        18.3          10    Sigma:  +1.64  Odds: 1 in    9.9    
    Neyman V1: mean                         1.12           0    Sigma:  +1.12  Odds: 1 in    3.8    
    Neyman V2: variance                    -1.45           0    Sigma:  -1.45  Odds: 1 in    6.8    
    Neyman V3: skewness                   -0.747           0    Sigma:  -0.75  Odds: 1 in    2.2    
    Neyman V4: kurtosis                    -2.41           0    Sigma:  -2.41  Odds: 1 in    62.    
    Neyman remainder: fine structure        23.1          30    Sigma:  -0.89  Odds: 1 in    2.7    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +1.64  Odds: 1 in    9.9    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Poisson distribution, rate = 17.1
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   17.10	   4.135	   17.10	  0.2418	 0.05848
1.000e+06	   17.09	   4.133	   17.08	  0.2418	 0.06238
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      3.000)   |-
[     3.000,      6.000)   |-
[     6.000,      9.000)   |##-
[     9.000,      12.00)   |############-
[     12.00,      15.00)   |#################################=
[     15.00,      18.00)   |##################################################
[     18.00,      21.00)   |###########################################-
[     21.00,      24.00)   |#######################=
[     24.00,      27.00)   |########=
[     27.00,      30.00)   |##-
[     30.00,      33.00)   |-
[     33.00,      36.00)   |-
[     36.00,      39.00)   |-
[     39.00,      42.00)   |-
[     42.00,      45.00)   |-
[     45.00,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  57.5          34    Sigma:  +2.45  Odds: 1 in    70.    
Neyman's smooth test                        15.7          10    Sigma:  +1.23  Odds: 1 in    4.6    
    Neyman V1: mean                        -1.24           0    Sigma:  -1.24  Odds: 1 in    4.7    
    Neyman V2: variance                   -0.625           0    Sigma:  -0.62  Odds: 1 in    1.9    
    Neyman V3: skewness                    0.031           0    Sigma:  +0.03  Odds: 1 in    1.0    
    Neyman V4: kurtosis                    0.629           0    Sigma:  +0.63  Odds: 1 in    1.9    
    Neyman remainder: fine structure        55.2          30    Sigma:  +2.71  Odds: 1 in 1.5e+02    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +1.23  Odds: 1 in    4.6    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Poisson distribution, rate = 100
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   100.0	   10.00	   100.0	  0.1000	 0.01000
1.000e+06	   100.0	   10.01	   100.2	  0.1035	0.008080
--------------------------------------------------------------------------------
( -Infinity,      55.00)   |
[     55.00,      60.00)   |-
[     60.00,      65.00)   |-
[     65.00,      70.00)   |-
[     70.00,      75.00)   |=
[     75.00,      80.00)   |###=
[     80.00,      85.00)   |##########=
[     85.00,      90.00)   |#######################-
[     90.00,      95.00)   |######################################=
[     95.00,      100.0)   |#################################################=
[     100.0,      105.0)   |##################################################
[     105.0,      110.0)   |#######################################-
[     110.0,      115.0)   |########################=
[     115.0,      120.0)   |############-
[     120.0,      125.0)   |#####-
[     125.0,      130.0)   |#=
[     130.0,      135.0)   |-
[     135.0,      140.0)   |-
[     140.0,      145.0)   |-
[     145.0,      150.0)   |-
[     150.0,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  60.9          83    Sigma:  -1.85  Odds: 1 in    15.    
Neyman's smooth test                        13.3          10    Sigma:  +0.82  Odds: 1 in    2.4    
    Neyman V1: mean                       0.0671           0    Sigma:  +0.07  Odds: 1 in    1.1    
    Neyman V2: variance                     1.13           0    Sigma:  +1.13  Odds: 1 in    3.9    
    Neyman V3: skewness                     1.34           0    Sigma:  +1.34  Odds: 1 in    5.6    
    Neyman V4: kurtosis                   -0.722           0    Sigma:  -0.72  Odds: 1 in    2.1    
    Neyman remainder: fine structure        57.2          79    Sigma:  -1.87  Odds: 1 in    16.    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +0.82  Odds: 1 in    2.4    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing Poisson distribution, rate = 5000
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   5000.	   70.71	   5000.	 0.01414	0.0002000
1.000e+06	   5000.	   70.68	   4995.	 0.01491	-0.003318
--------------------------------------------------------------------------------
( -Infinity,      4588.)   |
[     4588.,      4625.)   |-
[     4625.,      4662.)   |
[     4662.,      4699.)   |-
[     4699.,      4736.)   |-
[     4736.,      4773.)   |-
[     4773.,      4810.)   |=
[     4810.,      4847.)   |##=
[     4847.,      4884.)   |########=
[     4884.,      4921.)   |###################=
[     4921.,      4958.)   |###################################=
[     4958.,      4995.)   |################################################-
[     4995.,      5032.)   |##################################################
[     5032.,      5069.)   |#######################################=
[     5069.,      5106.)   |########################-
[     5106.,      5143.)   |###########-
[     5143.,      5180.)   |####-
[     5180.,      5217.)   |#-
[     5217.,      5254.)   |-
[     5254.,      5291.)   |-
[     5291.,      5328.)   |-
[     5328.,      5365.)   |-
[     5365.,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                   565         531    Sigma:  +1.03  Odds: 1 in    3.3    
Neyman's smooth test                        8.18          10    Sigma:  -0.28  Odds: 1 in    1.3    
    Neyman V1: mean                       -0.897           0    Sigma:  -0.90  Odds: 1 in    2.7    
    Neyman V2: variance                   -0.676           0    Sigma:  -0.68  Odds: 1 in    2.0    
    Neyman V3: skewness                    0.375           0    Sigma:  +0.38  Odds: 1 in    1.4    
    Neyman V4: kurtosis                   -0.721           0    Sigma:  -0.72  Odds: 1 in    2.1    
    Neyman remainder: fine structure         563         527    Sigma:  +1.10  Odds: 1 in    3.7    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.28  Odds: 1 in    1.3    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing dice (discrete uniform) distribution, a = 1, b = 6
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   3.500	   1.708	   2.917	   0.000	  -1.269
1.000e+06	   3.502	   1.707	   2.914	-0.001518	  -1.267
--------------------------------------------------------------------------------
( -Infinity,      1.000)   |
[     1.000,      1.500)   |#################################################=
[     1.500,      2.000)   |
[     2.000,      2.500)   |#################################################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |#################################################=
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################################=
[     4.500,      5.000)   |
[     5.000,      5.500)   |##################################################
[     5.500,      6.000)   |
[     6.000,      6.500)   |#################################################=
[     6.500,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  3.61           5    Sigma:  -0.27  Odds: 1 in    1.3    
Neyman's smooth test                        6.63          10    Sigma:  -0.71  Odds: 1 in    2.1    
    Neyman V1: mean                         1.24           0    Sigma:  +1.24  Odds: 1 in    4.6    
    Neyman V2: variance                    -1.23           0    Sigma:  -1.23  Odds: 1 in    4.6    
    Neyman V3: skewness                   0.0772           0    Sigma:  +0.08  Odds: 1 in    1.1    
    Neyman V4: kurtosis                   -0.151           0    Sigma:  -0.15  Odds: 1 in    1.1    
    Neyman remainder: fine structure       0.532           1    Sigma:  +0.09  Odds: 1 in    1.1    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.71  Odds: 1 in    2.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing dice (discrete uniform) distribution, a = -1, b = 5
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   2.000	   2.000	   4.000	   0.000	  -1.250
1.000e+06	   2.000	   1.998	   3.994	-0.0009034	  -1.248
--------------------------------------------------------------------------------
( -Infinity,     -1.000)   |
[    -1.000,    -0.5000)   |#################################################=
[   -0.5000,      0.000)   |
[     0.000,     0.5000)   |#################################################=
[    0.5000,      1.000)   |
[     1.000,      1.500)   |#################################################=
[     1.500,      2.000)   |
[     2.000,      2.500)   |#################################################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |##################################################
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################################=
[     4.500,      5.000)   |
[     5.000,      5.500)   |#################################################=
[     5.500,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  6.78           6    Sigma:  +0.41  Odds: 1 in    1.5    
Neyman's smooth test                        9.63          10    Sigma:  +0.07  Odds: 1 in    1.1    
    Neyman V1: mean                       -0.126           0    Sigma:  -0.13  Odds: 1 in    1.1    
    Neyman V2: variance                    -1.75           0    Sigma:  -1.75  Odds: 1 in    13.    
    Neyman V3: skewness                    -1.52           0    Sigma:  -1.52  Odds: 1 in    7.8    
    Neyman V4: kurtosis                   -0.116           0    Sigma:  -0.12  Odds: 1 in    1.1    
    Neyman remainder: fine structure        1.35           2    Sigma:  -0.03  Odds: 1 in    1.0    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +0.07  Odds: 1 in    1.1    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing discrete non-uniform distribution, n = 7
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   4.150	   1.768	   3.127	 -0.7704	 -0.3742
1.000e+06	   4.154	   1.767	   3.124	 -0.7736	 -0.3677
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |########-
[    0.5000,      1.000)   |
[     1.000,      1.500)   |########-
[     1.500,      2.000)   |
[     2.000,      2.500)   |################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |################=
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################-
[     4.500,      5.000)   |
[     5.000,      5.500)   |#################################-
[     5.500,      6.000)   |
[     6.000,      6.500)   |##################################################
[     6.500,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  9.33           6    Sigma:  +1.01  Odds: 1 in    3.2    
Neyman's smooth test                        11.9          10    Sigma:  +0.55  Odds: 1 in    1.7    
    Neyman V1: mean                         2.38           0    Sigma:  +2.38  Odds: 1 in    58.    
    Neyman V2: variance                    0.626           0    Sigma:  +0.63  Odds: 1 in    1.9    
    Neyman V3: skewness                  -0.0257           0    Sigma:  -0.03  Odds: 1 in    1.0    
    Neyman V4: kurtosis                    0.418           0    Sigma:  +0.42  Odds: 1 in    1.5    
    Neyman remainder: fine structure        3.11           2    Sigma:  +0.80  Odds: 1 in    2.4    
Combined assessment (Neyman only due to the discrete data):     Sigma:  +0.55  Odds: 1 in    1.7    Unremarkable
------------------------------------------------------------------------------------------------------------------------

Quality testing vose alias sampling, n = 7
Drawing 1000000 samples...
Expected vs actual:
Count   	Mean    	StdDev  	Variance	Skewness	Excess kurtosis
1.000e+06	   4.150	   1.768	   3.127	 -0.7704	 -0.3742
1.000e+06	   4.150	   1.768	   3.125	 -0.7694	 -0.3748
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |########-
[    0.5000,      1.000)   |
[     1.000,      1.500)   |########-
[     1.500,      2.000)   |
[     2.000,      2.500)   |################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |################=
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################-
[     4.500,      5.000)   |
[     5.000,      5.500)   |#################################-
[     5.500,      6.000)   |
[     6.000,      6.500)   |##################################################
[     6.500,   Infinity)   |
--------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
Goodness-of-fit test:                    Actual:   Expected:    Interpretation:
------------------------------------------------------------------------------------------------------------------------
Pearson's chi squared test                  5.51           6    Sigma:  +0.05  Odds: 1 in    1.0    
Neyman's smooth test                         6.9          10    Sigma:  -0.63  Odds: 1 in    1.9    
    Neyman V1: mean                       0.0277           0    Sigma:  +0.03  Odds: 1 in    1.0    
    Neyman V2: variance                   -0.918           0    Sigma:  -0.92  Odds: 1 in    2.8    
    Neyman V3: skewness                     0.75           0    Sigma:  +0.75  Odds: 1 in    2.2    
    Neyman V4: kurtosis                    0.335           0    Sigma:  +0.34  Odds: 1 in    1.4    
    Neyman remainder: fine structure           4           2    Sigma:  +1.10  Odds: 1 in    3.7    
Combined assessment (Neyman only due to the discrete data):     Sigma:  -0.63  Odds: 1 in    1.9    Unremarkable
------------------------------------------------------------------------------------------------------------------------
********************************************************************************
