WalleniusHypergeometricDistribution

WalleniusHypergeometricDistribution[n, nsucc, ntot, w]
represents a Wallenius noncentral hypergeometric distribution.

DetailsDetails

  • A Wallenius hypergeometric distribution gives the distribution of the number of successes in n dependent draws from a population of size containing successes with the odds ratio w.
  • The probability for integer value in a Wallenius hypergeometric distribution is equal to TemplateBox[{{n, _, {(, succ, )}}, x}, Binomial] TemplateBox[{{{n, _, {(, tot, )}}, -, {n, _, {(, succ, )}}}, {n, -, x}}, Binomial] int_0^1(1-t^(1/d))^(n-x) (1-t^(w/d))^xdt where .
  • WalleniusHypergeometricDistribution allows n, , and to be any integers such that , , and w is any positive real number.
  • WalleniusHypergeometricDistribution can be used with such functions as Mean, CDF, and RandomVariate.

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Probability density function:

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Cumulative distribution function:

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Mean does not have closed form but can be obtained numerically:

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Variance does not have closed form but can be obtained numerically:

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