Geometric Distribution

The Geometric Distribution, as implemented here, can be used to model the number of failures before the first success in a sequence of Bernoulli trials.

Assumptions

p is a valid probability (0 < p ≤ 1).

Use

mctad.geometric(p)

Inline Comments

mctad.geometric = function (p) {

Check that p is a valid probability (0 < p ≤ 1).

if (p <= 0 || p > 1.0) { return undefined; } var x = 0, pmf, cdf = 0, dfs = { mean: (1 - p)/p, median: undefined, // @todo: understand nonuniqueness as laid out at wikipedia page mode: [0.0], variance: (1.0 - p)/Math.pow(p, 2), skewness: (2 - p)/Math.sqrt(1 - p), entropy: (-(1.0 - p) * (Math.log(1.0 - p) / Math.LN2) - p * (Math.log(p) / Math.LN2)) / p, domain: { min: 0, max: Infinity }, range: { min: 0.0, max: 0.0 },

mctad.geometric(0.25).generate(100) will generate an Array of 100 random variables, distributed geometrically with a probability .25 of success.

generate: function (n) { var randomVariables = []; for (var k = 0; k < n; k++ ) { randomVariables.push(Math.floor(Math.log(mctad.getRandomArbitrary(0, 1)) / Math.log(1.0 - p))); } return randomVariables; } };

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

do { pmf = p * Math.pow(1.0 - p, x); cdf += pmf; dfs[x] = { pmf: pmf, cdf: cdf }; if (pmf > dfs.range.max) { dfs.range.max = 0.1 * Math.ceil(10 * pmf); } x++; } while (dfs[x - 1].cdf < 1.0 - mctad.ε); dfs.domain.max = x - 1;

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

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