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BUILT-IN MATHEMATICA SYMBOL
WalleniusHypergeometricDistribution
WalleniusHypergeometricDistribution[n, nsucc, ntot, w]
represents a Wallenius noncentral hypergeometric distribution.
Details
- 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](Files/WalleniusHypergeometricDistribution.en/4.png "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.
New in 8
