org.apache.commons.math3.distribution

Class ZipfDistribution.ZipfRejectionInversionSampler

java.lang.Object

org.apache.commons.math3.distribution.ZipfDistribution.ZipfRejectionInversionSampler

Enclosing class:

ZipfDistribution

static final class ZipfDistribution.ZipfRejectionInversionSampler
extends java.lang.Object

Utility class implementing a rejection inversion sampling method for a discrete, bounded Zipf distribution that is based on the method described in

Wolfgang Hörmann and Gerhard Derflinger "Rejection-inversion to generate variates from monotone discrete distributions." ACM Transactions on Modeling and Computer Simulation (TOMACS) 6.3 (1996): 169-184.

The paper describes an algorithm for exponents larger than 1 (Algorithm ZRI). The original method uses H(x) := (v + x)^(1 - q) / (1 - q) as the integral of the hat function. This function is undefined for q = 1, which is the reason for the limitation of the exponent. If instead the integral function H(x) := ((v + x)^(1 - q) - 1) / (1 - q) is used, for which a meaningful limit exists for q = 1, the method works for all positive exponents.

The following implementation uses v := 0 and generates integral numbers in the range [1, numberOfElements]. This is different to the original method where v is defined to be positive and numbers are taken from [0, i_max]. This explains why the implementation looks slightly different.

Since:

3.6

Field Summary

Fields

Modifier and Type	Field and Description
private double	exponent Exponent parameter of the distribution.
private double	hIntegralNumberOfElements Constant equal to hIntegral(numberOfElements + 0.5).
private double	hIntegralX1 Constant equal to hIntegral(1.5) - 1.
private int	numberOfElements Number of elements.
private double	s Constant equal to 2 - hIntegralInverse(hIntegral(2.5) - h(2).

Constructor Summary

Constructors

Constructor and Description
ZipfDistribution.ZipfRejectionInversionSampler(int numberOfElements, double exponent) Simple constructor.

Method Summary

Methods

Modifier and Type	Method and Description
private double	h(double x) h(x) := 1/x^exponent
(package private) static double	helper1(double x) Helper function that calculates log(1+x)/x.
(package private) static double	helper2(double x) Helper function to calculate (exp(x)-1)/x.
private double	hIntegral(double x) H(x) := (x^(1-exponent) - 1)/(1 - exponent), if exponent != 1 log(x), if exponent == 1 H(x) is an integral function of h(x), the derivative of H(x) is h(x).
private double	hIntegralInverse(double x) The inverse function of H(x).
(package private) int	sample(RandomGenerator random) Generate one integral number in the range [1, numberOfElements].

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

exponent

private final double exponent

Exponent parameter of the distribution.

numberOfElements

private final int numberOfElements

Number of elements.

hIntegralX1

private final double hIntegralX1

Constant equal to hIntegral(1.5) - 1.

hIntegralNumberOfElements

private final double hIntegralNumberOfElements

Constant equal to hIntegral(numberOfElements + 0.5).

s

private final double s

Constant equal to 2 - hIntegralInverse(hIntegral(2.5) - h(2).

Constructor Detail

ZipfDistribution.ZipfRejectionInversionSampler

ZipfDistribution.ZipfRejectionInversionSampler(int numberOfElements,
                                              double exponent)

Simple constructor.

Parameters:

numberOfElements - number of elements

exponent - exponent parameter of the distribution

Method Detail

sample

int sample(RandomGenerator random)

Generate one integral number in the range [1, numberOfElements].

Parameters:

random - random generator to use

Returns:

generated integral number in the range [1, numberOfElements]

hIntegral

private double hIntegral(double x)

H(x) :=

• (x^(1-exponent) - 1)/(1 - exponent), if exponent != 1
• log(x), if exponent == 1

H(x) is an integral function of h(x), the derivative of H(x) is h(x).

Parameters:

x - free parameter

Returns:

H(x)

h

private double h(double x)

h(x) := 1/x^exponent

Parameters:

x - free parameter

Returns:

h(x)

hIntegralInverse

private double hIntegralInverse(double x)

The inverse function of H(x).

Parameters:

x - free parameter

Returns:

y for which H(y) = x

helper1

static double helper1(double x)

Helper function that calculates log(1+x)/x.

A Taylor series expansion is used, if x is close to 0.

Parameters:

x - a value larger than or equal to -1

Returns:

log(1+x)/x

helper2

static double helper2(double x)

Helper function to calculate (exp(x)-1)/x.

A Taylor series expansion is used, if x is close to 0.

Parameters:

x - free parameter

Returns:

(exp(x)-1)/x if x is non-zero, or 1 if x=0