Safe Haskell	None
Language	Haskell98

Data.Random.Distribution

Synopsis

class Distribution d t where
class Distribution d t => PDF d t where
class Distribution d t => CDF d t where

Documentation

class Distribution d t where #

A Distribution is a data representation of a random variable's probability structure. For example, in Data.Random.Distribution.Normal, the Normal distribution is defined as:

data Normal a
    = StdNormal
    | Normal a a

Where the two parameters of the Normal data constructor are the mean and standard deviation of the random variable, respectively. To make use of the Normal type, one can convert it to an rvar and manipulate it or sample it directly:

x <- sample (rvar (Normal 10 2))
x <- sample (Normal 10 2)

A Distribution is typically more transparent than an RVar but less composable (precisely because of that transparency). There are several practical uses for types implementing Distribution:

Typically, a Distribution will expose several parameters of a standard mathematical model of a probability distribution, such as mean and std deviation for the normal distribution. Thus, they can be manipulated analytically using mathematical insights about the distributions they represent. For example, a collection of bernoulli variables could be simplified into a (hopefully) smaller collection of binomial variables.
Because they are generally just containers for parameters, they can be easily serialized to persistent storage or read from user-supplied configurations (eg, initialization data for a simulation).
If a type additionally implements the CDF subclass, which extends Distribution with a cumulative density function, an arbitrary random variable x can be tested against the distribution by testing fmap (cdf dist) x for uniformity.

On the other hand, most Distributions will not be closed under all the same operations as RVar (which, being a monad, has a fully turing-complete internal computational model). The sum of two uniformly-distributed variables, for example, is not uniformly distributed. To support general composition, the Distribution class defines a function rvar to construct the more-abstract and more-composable RVar representation of a random variable.

Methods

rvar :: d t -> RVar t #

Return a random variable with this distribution.

rvarT :: d t -> RVarT n t #

Return a random variable with the given distribution, pre-lifted to an arbitrary RVarT. Any arbitrary RVar can also be converted to an 'RVarT m' for an arbitrary m, using either lift or sample.

Instances

Distribution StdUniform Bool #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Bool -> RVar Bool # rvarT :: StdUniform Bool -> RVarT n Bool #
Distribution StdUniform Char #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Char -> RVar Char # rvarT :: StdUniform Char -> RVarT n Char #
Distribution StdUniform Double #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Double -> RVar Double # rvarT :: StdUniform Double -> RVarT n Double #
Distribution StdUniform Float #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Float -> RVar Float # rvarT :: StdUniform Float -> RVarT n Float #
Distribution StdUniform Int #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Int -> RVar Int # rvarT :: StdUniform Int -> RVarT n Int #
Distribution StdUniform Int8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Int8 -> RVar Int8 # rvarT :: StdUniform Int8 -> RVarT n Int8 #
Distribution StdUniform Int16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Int16 -> RVar Int16 # rvarT :: StdUniform Int16 -> RVarT n Int16 #
Distribution StdUniform Int32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Int32 -> RVar Int32 # rvarT :: StdUniform Int32 -> RVarT n Int32 #
Distribution StdUniform Int64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Int64 -> RVar Int64 # rvarT :: StdUniform Int64 -> RVarT n Int64 #
Distribution StdUniform Ordering #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Ordering -> RVar Ordering # rvarT :: StdUniform Ordering -> RVarT n Ordering #
Distribution StdUniform Word #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Word -> RVar Word # rvarT :: StdUniform Word -> RVarT n Word #
Distribution StdUniform Word8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Word8 -> RVar Word8 # rvarT :: StdUniform Word8 -> RVarT n Word8 #
Distribution StdUniform Word16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Word16 -> RVar Word16 # rvarT :: StdUniform Word16 -> RVarT n Word16 #
Distribution StdUniform Word32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Word32 -> RVar Word32 # rvarT :: StdUniform Word32 -> RVarT n Word32 #
Distribution StdUniform Word64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform Word64 -> RVar Word64 # rvarT :: StdUniform Word64 -> RVarT n Word64 #
Distribution StdUniform () #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform () -> RVar () # rvarT :: StdUniform () -> RVarT n () #
Distribution Uniform Bool #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Bool -> RVar Bool # rvarT :: Uniform Bool -> RVarT n Bool #
Distribution Uniform Char #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Char -> RVar Char # rvarT :: Uniform Char -> RVarT n Char #
Distribution Uniform Double #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Double -> RVar Double # rvarT :: Uniform Double -> RVarT n Double #
Distribution Uniform Float #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Float -> RVar Float # rvarT :: Uniform Float -> RVarT n Float #
Distribution Uniform Int #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Int -> RVar Int # rvarT :: Uniform Int -> RVarT n Int #
Distribution Uniform Int8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Int8 -> RVar Int8 # rvarT :: Uniform Int8 -> RVarT n Int8 #
Distribution Uniform Int16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Int16 -> RVar Int16 # rvarT :: Uniform Int16 -> RVarT n Int16 #
Distribution Uniform Int32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Int32 -> RVar Int32 # rvarT :: Uniform Int32 -> RVarT n Int32 #
Distribution Uniform Int64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Int64 -> RVar Int64 # rvarT :: Uniform Int64 -> RVarT n Int64 #
Distribution Uniform Integer #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Integer -> RVar Integer # rvarT :: Uniform Integer -> RVarT n Integer #
Distribution Uniform Ordering #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Ordering -> RVar Ordering # rvarT :: Uniform Ordering -> RVarT n Ordering #
Distribution Uniform Word #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Word -> RVar Word # rvarT :: Uniform Word -> RVarT n Word #
Distribution Uniform Word8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Word8 -> RVar Word8 # rvarT :: Uniform Word8 -> RVarT n Word8 #
Distribution Uniform Word16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Word16 -> RVar Word16 # rvarT :: Uniform Word16 -> RVarT n Word16 #
Distribution Uniform Word32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Word32 -> RVar Word32 # rvarT :: Uniform Word32 -> RVarT n Word32 #
Distribution Uniform Word64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform Word64 -> RVar Word64 # rvarT :: Uniform Word64 -> RVarT n Word64 #
Distribution Uniform () #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform () -> RVar () # rvarT :: Uniform () -> RVarT n () #
(Floating a, Distribution StdUniform a) => Distribution Weibull a #
Instance details Defined in Data.Random.Distribution.Weibull Methods rvar :: Weibull a -> RVar a # rvarT :: Weibull a -> RVarT n a #
(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a #
Instance details Defined in Data.Random.Distribution.Triangular Methods rvar :: Triangular a -> RVar a # rvarT :: Triangular a -> RVarT n a #
(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a #
Instance details Defined in Data.Random.Distribution.StretchedExponential Methods rvar :: StretchedExponential a -> RVar a # rvarT :: StretchedExponential a -> RVarT n a #
(RealFloat a, Distribution StdUniform a) => Distribution Rayleigh a #
Instance details Defined in Data.Random.Distribution.Rayleigh Methods rvar :: Rayleigh a -> RVar a # rvarT :: Rayleigh a -> RVarT n a #
Distribution Normal Double #
Instance details Defined in Data.Random.Distribution.Normal Methods rvar :: Normal Double -> RVar Double # rvarT :: Normal Double -> RVarT n Double #
Distribution Normal Float #
Instance details Defined in Data.Random.Distribution.Normal Methods rvar :: Normal Float -> RVar Float # rvarT :: Normal Float -> RVarT n Float #
(Floating a, Ord a, Distribution Normal a, Distribution StdUniform a) => Distribution Gamma a #
Instance details Defined in Data.Random.Distribution.Gamma Methods rvar :: Gamma a -> RVar a # rvarT :: Gamma a -> RVarT n a #
(Floating a, Distribution StdUniform a) => Distribution Exponential a #
Instance details Defined in Data.Random.Distribution.Exponential Methods rvar :: Exponential a -> RVar a # rvarT :: Exponential a -> RVarT n a #
(Fractional t, Distribution Gamma t) => Distribution ChiSquare t #
Instance details Defined in Data.Random.Distribution.ChiSquare Methods rvar :: ChiSquare t -> RVar t # rvarT :: ChiSquare t -> RVarT n t #
(Floating a, Distribution Normal a, Distribution ChiSquare a) => Distribution T a #
Instance details Defined in Data.Random.Distribution.T Methods rvar :: T a -> RVar a # rvarT :: T a -> RVarT n a #
Distribution Beta Double #
Instance details Defined in Data.Random.Distribution.Beta Methods rvar :: Beta Double -> RVar Double # rvarT :: Beta Double -> RVarT n Double #
Distribution Beta Float #
Instance details Defined in Data.Random.Distribution.Beta Methods rvar :: Beta Float -> RVar Float # rvarT :: Beta Float -> RVarT n Float #
(Floating a, Distribution StdUniform a) => Distribution Pareto a #
Instance details Defined in Data.Random.Distribution.Pareto Methods rvar :: Pareto a -> RVar a # rvarT :: Pareto a -> RVarT n a #
HasResolution r => Distribution StdUniform (Fixed r) #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: StdUniform (Fixed r) -> RVar (Fixed r) # rvarT :: StdUniform (Fixed r) -> RVarT n (Fixed r) #
HasResolution r => Distribution Uniform (Fixed r) #
Instance details Defined in Data.Random.Distribution.Uniform Methods rvar :: Uniform (Fixed r) -> RVar (Fixed r) # rvarT :: Uniform (Fixed r) -> RVarT n (Fixed r) #
(Ord a, Fractional a, Distribution StdUniform a) => Distribution StdSimplex [a] #
Instance details Defined in Data.Random.Distribution.Simplex Methods rvar :: StdSimplex [a] -> RVar [a] # rvarT :: StdSimplex [a] -> RVarT n [a] #
(Fractional a, Distribution Gamma a) => Distribution Dirichlet [a] #
Instance details Defined in Data.Random.Distribution.Dirichlet Methods rvar :: Dirichlet [a] -> RVar [a] # rvarT :: Dirichlet [a] -> RVarT n [a] #
(Num t, Ord t, Vector v t) => Distribution (Ziggurat v) t #
Instance details Defined in Data.Random.Distribution.Ziggurat Methods rvar :: Ziggurat v t -> RVar t # rvarT :: Ziggurat v t -> RVarT n t #
(Integral a, Floating b, Ord b, Distribution Normal b, Distribution StdUniform b) => Distribution (Erlang a) b #
Instance details Defined in Data.Random.Distribution.Gamma Methods rvar :: Erlang a b -> RVar b # rvarT :: Erlang a b -> RVarT n b #
(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a #
Instance details Defined in Data.Random.Distribution.Categorical Methods rvar :: Categorical p a -> RVar a # rvarT :: Categorical p a -> RVarT n a #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Integer #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Integer -> RVar Integer # rvarT :: Binomial b Integer -> RVarT n Integer #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Int -> RVar Int # rvarT :: Binomial b Int -> RVarT n Int #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int8 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Int8 -> RVar Int8 # rvarT :: Binomial b Int8 -> RVarT n Int8 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int16 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Int16 -> RVar Int16 # rvarT :: Binomial b Int16 -> RVarT n Int16 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int32 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Int32 -> RVar Int32 # rvarT :: Binomial b Int32 -> RVarT n Int32 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int64 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Int64 -> RVar Int64 # rvarT :: Binomial b Int64 -> RVarT n Int64 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Word -> RVar Word # rvarT :: Binomial b Word -> RVarT n Word #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word8 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Word8 -> RVar Word8 # rvarT :: Binomial b Word8 -> RVarT n Word8 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word16 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Word16 -> RVar Word16 # rvarT :: Binomial b Word16 -> RVarT n Word16 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word32 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Word32 -> RVar Word32 # rvarT :: Binomial b Word32 -> RVarT n Word32 #
(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word64 #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Word64 -> RVar Word64 # rvarT :: Binomial b Word64 -> RVarT n Word64 #
Distribution (Binomial b) Integer => Distribution (Binomial b) Float #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Float -> RVar Float # rvarT :: Binomial b Float -> RVarT n Float #
Distribution (Binomial b) Integer => Distribution (Binomial b) Double #
Instance details Defined in Data.Random.Distribution.Binomial Methods rvar :: Binomial b Double -> RVar Double # rvarT :: Binomial b Double -> RVarT n Double #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Integer) b, Distribution (Binomial b) Integer) => Distribution (Poisson b) Integer #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Integer -> RVar Integer # rvarT :: Poisson b Integer -> RVarT n Integer #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int) b, Distribution (Binomial b) Int) => Distribution (Poisson b) Int #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Int -> RVar Int # rvarT :: Poisson b Int -> RVarT n Int #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int8) b, Distribution (Binomial b) Int8) => Distribution (Poisson b) Int8 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Int8 -> RVar Int8 # rvarT :: Poisson b Int8 -> RVarT n Int8 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int16) b, Distribution (Binomial b) Int16) => Distribution (Poisson b) Int16 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Int16 -> RVar Int16 # rvarT :: Poisson b Int16 -> RVarT n Int16 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int32) b, Distribution (Binomial b) Int32) => Distribution (Poisson b) Int32 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Int32 -> RVar Int32 # rvarT :: Poisson b Int32 -> RVarT n Int32 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int64) b, Distribution (Binomial b) Int64) => Distribution (Poisson b) Int64 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Int64 -> RVar Int64 # rvarT :: Poisson b Int64 -> RVarT n Int64 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word) b, Distribution (Binomial b) Word) => Distribution (Poisson b) Word #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Word -> RVar Word # rvarT :: Poisson b Word -> RVarT n Word #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word8) b, Distribution (Binomial b) Word8) => Distribution (Poisson b) Word8 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Word8 -> RVar Word8 # rvarT :: Poisson b Word8 -> RVarT n Word8 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word16) b, Distribution (Binomial b) Word16) => Distribution (Poisson b) Word16 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Word16 -> RVar Word16 # rvarT :: Poisson b Word16 -> RVarT n Word16 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word32) b, Distribution (Binomial b) Word32) => Distribution (Poisson b) Word32 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Word32 -> RVar Word32 # rvarT :: Poisson b Word32 -> RVarT n Word32 #
(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word64) b, Distribution (Binomial b) Word64) => Distribution (Poisson b) Word64 #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Word64 -> RVar Word64 # rvarT :: Poisson b Word64 -> RVarT n Word64 #
Distribution (Poisson b) Integer => Distribution (Poisson b) Float #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Float -> RVar Float # rvarT :: Poisson b Float -> RVarT n Float #
Distribution (Poisson b) Integer => Distribution (Poisson b) Double #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Double -> RVar Double # rvarT :: Poisson b Double -> RVarT n Double #
(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Bool -> RVar Bool # rvarT :: Bernoulli b Bool -> RVarT n Bool #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Integer #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Integer -> RVar Integer # rvarT :: Bernoulli b Integer -> RVarT n Integer #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Int -> RVar Int # rvarT :: Bernoulli b Int -> RVarT n Int #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int8 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Int8 -> RVar Int8 # rvarT :: Bernoulli b Int8 -> RVarT n Int8 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int16 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Int16 -> RVar Int16 # rvarT :: Bernoulli b Int16 -> RVarT n Int16 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int32 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Int32 -> RVar Int32 # rvarT :: Bernoulli b Int32 -> RVarT n Int32 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int64 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Int64 -> RVar Int64 # rvarT :: Bernoulli b Int64 -> RVarT n Int64 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Word -> RVar Word # rvarT :: Bernoulli b Word -> RVarT n Word #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word8 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Word8 -> RVar Word8 # rvarT :: Bernoulli b Word8 -> RVarT n Word8 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word16 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Word16 -> RVar Word16 # rvarT :: Bernoulli b Word16 -> RVarT n Word16 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word32 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Word32 -> RVar Word32 # rvarT :: Bernoulli b Word32 -> RVarT n Word32 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word64 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Word64 -> RVar Word64 # rvarT :: Bernoulli b Word64 -> RVarT n Word64 #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Float #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Float -> RVar Float # rvarT :: Bernoulli b Float -> RVarT n Float #
Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Double #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b Double -> RVar Double # rvarT :: Bernoulli b Double -> RVarT n Double #
(Num a, Eq a, Fractional p, Distribution (Binomial p) a) => Distribution (Multinomial p) [a] #
Instance details Defined in Data.Random.Distribution.Multinomial Methods rvar :: Multinomial p [a] -> RVar [a] # rvarT :: Multinomial p [a] -> RVarT n [a] #
(Distribution (Bernoulli b) Bool, RealFloat a) => Distribution (Bernoulli b) (Complex a) #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b (Complex a) -> RVar (Complex a) # rvarT :: Bernoulli b (Complex a) -> RVarT n (Complex a) #
(Distribution (Bernoulli b) Bool, Integral a) => Distribution (Bernoulli b) (Ratio a) #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods rvar :: Bernoulli b (Ratio a) -> RVar (Ratio a) # rvarT :: Bernoulli b (Ratio a) -> RVarT n (Ratio a) #

class Distribution d t => PDF d t where #

Methods

pdf :: d t -> t -> Double #

logPdf :: d t -> t -> Double #

Instances

PDF StdUniform Double #
Instance details Defined in Data.Random.Distribution.Uniform Methods pdf :: StdUniform Double -> Double -> Double # logPdf :: StdUniform Double -> Double -> Double #
PDF StdUniform Float #
Instance details Defined in Data.Random.Distribution.Uniform Methods pdf :: StdUniform Float -> Float -> Double # logPdf :: StdUniform Float -> Float -> Double #
(Real a, Floating a, Distribution Normal a) => PDF Normal a #
Instance details Defined in Data.Random.Distribution.Normal Methods pdf :: Normal a -> a -> Double # logPdf :: Normal a -> a -> Double #
PDF Beta Double #
Instance details Defined in Data.Random.Distribution.Beta Methods pdf :: Beta Double -> Double -> Double # logPdf :: Beta Double -> Double -> Double #
PDF Beta Float #
Instance details Defined in Data.Random.Distribution.Beta Methods pdf :: Beta Float -> Float -> Double # logPdf :: Beta Float -> Float -> Double #
(Real b, Distribution (Binomial b) Integer) => PDF (Binomial b) Integer #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Integer -> Integer -> Double # logPdf :: Binomial b Integer -> Integer -> Double #
(Real b, Distribution (Binomial b) Int) => PDF (Binomial b) Int #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Int -> Int -> Double # logPdf :: Binomial b Int -> Int -> Double #
(Real b, Distribution (Binomial b) Int8) => PDF (Binomial b) Int8 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Int8 -> Int8 -> Double # logPdf :: Binomial b Int8 -> Int8 -> Double #
(Real b, Distribution (Binomial b) Int16) => PDF (Binomial b) Int16 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Int16 -> Int16 -> Double # logPdf :: Binomial b Int16 -> Int16 -> Double #
(Real b, Distribution (Binomial b) Int32) => PDF (Binomial b) Int32 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Int32 -> Int32 -> Double # logPdf :: Binomial b Int32 -> Int32 -> Double #
(Real b, Distribution (Binomial b) Int64) => PDF (Binomial b) Int64 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Int64 -> Int64 -> Double # logPdf :: Binomial b Int64 -> Int64 -> Double #
(Real b, Distribution (Binomial b) Word) => PDF (Binomial b) Word #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Word -> Word -> Double # logPdf :: Binomial b Word -> Word -> Double #
(Real b, Distribution (Binomial b) Word8) => PDF (Binomial b) Word8 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Word8 -> Word8 -> Double # logPdf :: Binomial b Word8 -> Word8 -> Double #
(Real b, Distribution (Binomial b) Word16) => PDF (Binomial b) Word16 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Word16 -> Word16 -> Double # logPdf :: Binomial b Word16 -> Word16 -> Double #
(Real b, Distribution (Binomial b) Word32) => PDF (Binomial b) Word32 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Word32 -> Word32 -> Double # logPdf :: Binomial b Word32 -> Word32 -> Double #
(Real b, Distribution (Binomial b) Word64) => PDF (Binomial b) Word64 #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Word64 -> Word64 -> Double # logPdf :: Binomial b Word64 -> Word64 -> Double #
PDF (Binomial b) Integer => PDF (Binomial b) Float #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Float -> Float -> Double # logPdf :: Binomial b Float -> Float -> Double #
PDF (Binomial b) Integer => PDF (Binomial b) Double #
Instance details Defined in Data.Random.Distribution.Binomial Methods pdf :: Binomial b Double -> Double -> Double # logPdf :: Binomial b Double -> Double -> Double #

class Distribution d t => CDF d t where #

Minimal complete definition

cdf

Methods

cdf :: d t -> t -> Double #

Return the cumulative distribution function of this distribution. That is, a function taking x :: t to the probability that the next sample will return a value less than or equal to x, according to some order or partial order (not necessarily an obvious one).

In the case where t is an instance of Ord, cdf should correspond to the CDF with respect to that order.

In other cases, cdf is only required to satisfy the following law: fmap (cdf d) (rvar d) must be uniformly distributed over (0,1). Inclusion of either endpoint is optional, though the preferred range is (0,1].

Note that this definition requires that cdf for a product type should _not_ be a joint CDF as commonly defined, as that definition violates both conditions. Instead, it should be a univariate CDF over the product type. That is, it should represent the CDF with respect to the lexicographic order of the product.

The present specification is probably only really useful for testing conformance of a variable to its target distribution, and I am open to suggestions for more-useful specifications (especially with regard to the interaction with product types).

Instances

CDF StdUniform Bool #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Bool -> Bool -> Double #
CDF StdUniform Char #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Char -> Char -> Double #
CDF StdUniform Double #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Double -> Double -> Double #
CDF StdUniform Float #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Float -> Float -> Double #
CDF StdUniform Int #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Int -> Int -> Double #
CDF StdUniform Int8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Int8 -> Int8 -> Double #
CDF StdUniform Int16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Int16 -> Int16 -> Double #
CDF StdUniform Int32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Int32 -> Int32 -> Double #
CDF StdUniform Int64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Int64 -> Int64 -> Double #
CDF StdUniform Ordering #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Ordering -> Ordering -> Double #
CDF StdUniform Word #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Word -> Word -> Double #
CDF StdUniform Word8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Word8 -> Word8 -> Double #
CDF StdUniform Word16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Word16 -> Word16 -> Double #
CDF StdUniform Word32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Word32 -> Word32 -> Double #
CDF StdUniform Word64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform Word64 -> Word64 -> Double #
CDF StdUniform () #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform () -> () -> Double #
CDF Uniform Bool #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Bool -> Bool -> Double #
CDF Uniform Char #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Char -> Char -> Double #
CDF Uniform Double #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Double -> Double -> Double #
CDF Uniform Float #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Float -> Float -> Double #
CDF Uniform Int #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Int -> Int -> Double #
CDF Uniform Int8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Int8 -> Int8 -> Double #
CDF Uniform Int16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Int16 -> Int16 -> Double #
CDF Uniform Int32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Int32 -> Int32 -> Double #
CDF Uniform Int64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Int64 -> Int64 -> Double #
CDF Uniform Integer #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Integer -> Integer -> Double #
CDF Uniform Ordering #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Ordering -> Ordering -> Double #
CDF Uniform Word #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Word -> Word -> Double #
CDF Uniform Word8 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Word8 -> Word8 -> Double #
CDF Uniform Word16 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Word16 -> Word16 -> Double #
CDF Uniform Word32 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Word32 -> Word32 -> Double #
CDF Uniform Word64 #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform Word64 -> Word64 -> Double #
CDF Uniform () #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform () -> () -> Double #
(Real a, Distribution Weibull a) => CDF Weibull a #
Instance details Defined in Data.Random.Distribution.Weibull Methods cdf :: Weibull a -> a -> Double #
(RealFrac a, Distribution Triangular a) => CDF Triangular a #
Instance details Defined in Data.Random.Distribution.Triangular Methods cdf :: Triangular a -> a -> Double #
(Real a, Distribution StretchedExponential a) => CDF StretchedExponential a #
Instance details Defined in Data.Random.Distribution.StretchedExponential Methods cdf :: StretchedExponential a -> a -> Double #
(Real a, Distribution Rayleigh a) => CDF Rayleigh a #
Instance details Defined in Data.Random.Distribution.Rayleigh Methods cdf :: Rayleigh a -> a -> Double #
(Real a, Distribution Normal a) => CDF Normal a #
Instance details Defined in Data.Random.Distribution.Normal Methods cdf :: Normal a -> a -> Double #
(Real a, Distribution Gamma a) => CDF Gamma a #
Instance details Defined in Data.Random.Distribution.Gamma Methods cdf :: Gamma a -> a -> Double #
(Real a, Distribution Exponential a) => CDF Exponential a #
Instance details Defined in Data.Random.Distribution.Exponential Methods cdf :: Exponential a -> a -> Double #
(Real t, Distribution ChiSquare t) => CDF ChiSquare t #
Instance details Defined in Data.Random.Distribution.ChiSquare Methods cdf :: ChiSquare t -> t -> Double #
(Real a, Distribution T a) => CDF T a #
Instance details Defined in Data.Random.Distribution.T Methods cdf :: T a -> a -> Double #
(Real a, Distribution Pareto a) => CDF Pareto a #
Instance details Defined in Data.Random.Distribution.Pareto Methods cdf :: Pareto a -> a -> Double #
HasResolution r => CDF StdUniform (Fixed r) #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: StdUniform (Fixed r) -> Fixed r -> Double #
HasResolution r => CDF Uniform (Fixed r) #
Instance details Defined in Data.Random.Distribution.Uniform Methods cdf :: Uniform (Fixed r) -> Fixed r -> Double #
(Integral a, Real b, Distribution (Erlang a) b) => CDF (Erlang a) b #
Instance details Defined in Data.Random.Distribution.Gamma Methods cdf :: Erlang a b -> b -> Double #
(Real b, Distribution (Binomial b) Integer) => CDF (Binomial b) Integer #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Integer -> Integer -> Double #
(Real b, Distribution (Binomial b) Int) => CDF (Binomial b) Int #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Int -> Int -> Double #
(Real b, Distribution (Binomial b) Int8) => CDF (Binomial b) Int8 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Int8 -> Int8 -> Double #
(Real b, Distribution (Binomial b) Int16) => CDF (Binomial b) Int16 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Int16 -> Int16 -> Double #
(Real b, Distribution (Binomial b) Int32) => CDF (Binomial b) Int32 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Int32 -> Int32 -> Double #
(Real b, Distribution (Binomial b) Int64) => CDF (Binomial b) Int64 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Int64 -> Int64 -> Double #
(Real b, Distribution (Binomial b) Word) => CDF (Binomial b) Word #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Word -> Word -> Double #
(Real b, Distribution (Binomial b) Word8) => CDF (Binomial b) Word8 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Word8 -> Word8 -> Double #
(Real b, Distribution (Binomial b) Word16) => CDF (Binomial b) Word16 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Word16 -> Word16 -> Double #
(Real b, Distribution (Binomial b) Word32) => CDF (Binomial b) Word32 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Word32 -> Word32 -> Double #
(Real b, Distribution (Binomial b) Word64) => CDF (Binomial b) Word64 #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Word64 -> Word64 -> Double #
CDF (Binomial b) Integer => CDF (Binomial b) Float #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Float -> Float -> Double #
CDF (Binomial b) Integer => CDF (Binomial b) Double #
Instance details Defined in Data.Random.Distribution.Binomial Methods cdf :: Binomial b Double -> Double -> Double #
(Real b, Distribution (Poisson b) Integer) => CDF (Poisson b) Integer #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Integer -> Integer -> Double #
(Real b, Distribution (Poisson b) Int) => CDF (Poisson b) Int #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Int -> Int -> Double #
(Real b, Distribution (Poisson b) Int8) => CDF (Poisson b) Int8 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Int8 -> Int8 -> Double #
(Real b, Distribution (Poisson b) Int16) => CDF (Poisson b) Int16 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Int16 -> Int16 -> Double #
(Real b, Distribution (Poisson b) Int32) => CDF (Poisson b) Int32 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Int32 -> Int32 -> Double #
(Real b, Distribution (Poisson b) Int64) => CDF (Poisson b) Int64 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Int64 -> Int64 -> Double #
(Real b, Distribution (Poisson b) Word) => CDF (Poisson b) Word #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Word -> Word -> Double #
(Real b, Distribution (Poisson b) Word8) => CDF (Poisson b) Word8 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Word8 -> Word8 -> Double #
(Real b, Distribution (Poisson b) Word16) => CDF (Poisson b) Word16 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Word16 -> Word16 -> Double #
(Real b, Distribution (Poisson b) Word32) => CDF (Poisson b) Word32 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Word32 -> Word32 -> Double #
(Real b, Distribution (Poisson b) Word64) => CDF (Poisson b) Word64 #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Word64 -> Word64 -> Double #
CDF (Poisson b) Integer => CDF (Poisson b) Float #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Float -> Float -> Double #
CDF (Poisson b) Integer => CDF (Poisson b) Double #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Double -> Double -> Double #
(Distribution (Bernoulli b) Bool, Real b) => CDF (Bernoulli b) Bool #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Bool -> Bool -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Integer #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Integer -> Integer -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Int -> Int -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int8 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Int8 -> Int8 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int16 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Int16 -> Int16 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int32 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Int32 -> Int32 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int64 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Int64 -> Int64 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Word -> Word -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word8 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Word8 -> Word8 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word16 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Word16 -> Word16 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word32 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Word32 -> Word32 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word64 #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Word64 -> Word64 -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Float #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Float -> Float -> Double #
CDF (Bernoulli b) Bool => CDF (Bernoulli b) Double #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b Double -> Double -> Double #
(CDF (Bernoulli b) Bool, RealFloat a) => CDF (Bernoulli b) (Complex a) #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b (Complex a) -> Complex a -> Double #
(CDF (Bernoulli b) Bool, Integral a) => CDF (Bernoulli b) (Ratio a) #
Instance details Defined in Data.Random.Distribution.Bernoulli Methods cdf :: Bernoulli b (Ratio a) -> Ratio a -> Double #