BUILT-IN MATHEMATICA SYMBOL

FisherHypergeometricDistribution

represents a Fisher noncentral hypergeometric distribution.

MORE INFORMATION

A Fisher hypergeometric distribution gives the distribution of the number of successes in n independent draws from a population of size containing successes with the odds ratio w.

FisherHypergeometricDistribution allows n, , and to be any integers such that , and , and w is any positive real number.

FisherHypergeometricDistribution can be used with such functions as Mean, CDF, and RandomVariate.

EXAMPLES

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Basic Examples (3)

Probability density function:

Cumulative distribution function:

Mean:

Probability density function:

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Cumulative distribution function:

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Mean:

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Scope (5)

Generate a set of pseudorandom numbers that are hypergeometrically distributed:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Different moments with closed forms as functions of parameters:

Moment:

CentralMoment:

FactorialMoment:

Closed form for symbolic order:

Cumulant:

Hazard function:

Quantile function:

Applications (2)

CDF of FisherHypergeometricDistribution is an example of a right continuous function:

An urn contains

red balls of weight

and

blue balls of weight

. With

balls drawn independently, the probability of drawing a red or blue ball depends on its weight. If

,

, and

, find the distribution of the number of red balls drawn:

Find the probability that at least 3 red balls were drawn:

Find the average number of red balls:

Simulate the number of red balls in 30 consecutive samples of 12:

Properties & Relations (3)

Relationships to other distributions:

HypergeometricDistribution is a special case:

FisherHypergeometricDistribution can be obtained from two independent binomial variates conditioning on their total: