Hypergeometric Distribution

(discrete probability dist. for equations)

Usage:

HypergeometricDist (k, n, s, N)

Definition:

binomial (s,k) binomial (N-s, n-k) / binomial (N,n)

where binomial is the binomial coefficient

Required:

N ⋝ 0    0 ⋜ n ⋜ N     0 ⋜ s ⋜ N

k, N, n and s are integers

Support:

0 ⋜ k ⋜ n

Moments:

μ = n s / N

σ^2 = n s (1-s/N) (N-n) / [N (N-1)]

γ1 = (N-2s) (N-2n) sqrt (N-1) / [(N-2) sqrt (n s (N-s) (N-n))]

β2 = N^2 (N-1)/[(N-2)(N-3) n s (N-s)(N-n)] [N (N+1) - 6n (N-n) + 3s (N-s)/N^2 [N^2 (n-2) - N n^2 + 6n (N-n)]]