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)]] |
This provides the probability that there are k "successes" in a random sample of size n, selected (without replacement) from N items of which s are labeled "success" and N-s labeled "failure".
It is used in place of the binomial distribution for situations which sample without replacement.
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