The hypergeometric distribution
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The hypergeometric distribution describes the probability of
successes in draws
from a finite population size containing successes
without replacement. This contrasts with the binomial
distribution which describes the probability of successes
in draws with
replacement
Distribution name

Hypergeometric
distribution

Common notation


Parameters

=
population size, integral ()
=
sample size, integral ()
=
number of tagged items, integral ()

Domain


Probability mass
function


Cumulative distribution
function

where
is the
generalised hypergeometric function, i.e.
and involves the
rising factorial or Pochhammer notation, i.e. and

Mean


Variance


Skewness


(Excess) kurtosis

where

Characteristic function


Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “hypergeometric”.
For details of other supported probability distributions see here.
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