Bayesian Statistics: An Introduction, 4th Edition

A.14 Hypergeometric distribution

X has a hypergeometric distribution of population size N, index n and parameter π, denoted

if it has a discrete distribution with density

The mean and variance are

Because

we see that p(X+1)> p(X) if and only if

and hence that if, as is usually the case, N is fairly large, if and only if

Hence, the mode occurs very close to the binomial value

As this distribution approaches the binomial distribution .

Tables of it can be found in Lieberman and Owen (1961).