Hypergeometric Distribution

The Hypergeometric Distribution describes the probability of k successes in n draws without replacement from a finite population of size N containing exactly K successes. It's commonly used in statistical quality control.

Assumptions

N, K, and n are positive Integers with K ≤ N, n ≤ K.

Use

mctad.hypergeometric(N, K, n)

Inline Comments

mctad.hypergeometric = function (N, K, n) {

Check that N, K, and n are positive Integers, with K ≤ N, n ≤ N.

if (!mctad.isInteger(N) || !mctad.isInteger(K) || !mctad.isInteger(n) || N < 0 || K < 0 || n < 0 || K > N || n > N) { return undefined; } var k = 0, pmf, cdf = 0, dfs = { mean: n * K / N, median: undefined, mode: [Math.floor(((n + 1) * (K + 1)) / (N + 2))], variance: n * (K / N) * ((N - K) / N) * ((N - n) / (N - 1)), skewness: ((N - 2 * K) * Math.sqrt(N - 1) * (N - 2 * n)) / (Math.sqrt(n * K * (N - K) * (N - n)) * (N - 2)), entropy: undefined, domain: { min: 0, max: K }, range: { min: 0.0, max: 0.0 }

TODO: generate: function (n) { var randomVariables = []; return randomVariables; }

};

Iterate over the domain, calculating the probability mass and cumulative distribution functions.

for (k = 0; k <= n; k++) { pmf = (this.combination(K, k) * this.combination(N - K, n - k)) / this.combination(N, n); cdf += pmf; dfs[k] = { pmf: pmf, cdf: cdf }; if (pmf > dfs.range.max) { dfs.range.max = 0.1 * Math.ceil(10 * pmf); } }

Mix in the convenience methods for p(x) and F(x).

mctad.extend(dfs, mctad.discreteMixins); return dfs; };