Weibull Distribution

Assumptions

λ and k are strictly positive real numbers; λ may be thought of as a scale parameter, k as a shape parameter.

Use

mctad.weibull(λ, k)

Inline Comments

mctad.weibull = function (λ, k) {

Check that λ > 0 and k > 0.

if (λ < 0 || k < 0) { return undefined; } var dfs = { mean: λ * mctad.Γ(1 + 1 / k), median: λ * Math.pow(Math.log(2), 1 / k), mode: function () { if (k >= 1) { return λ * Math.pow((k - 1) / k, 1 / k); } else { return 0.0; } }(), variance: Math.pow(λ, 2) * ( mctad.Γ(1 + 2 / k) - Math.pow(mctad.Γ(1 + 1 / k), 2)), skewness: undefined, // @todo circle back for this entropy: undefined, // @todo circle back for this domain: { min: 0, max: Infinity }, range: { min: 0, max: Infinity },

mctad.weibull(1.5).generate(100) will generate an Array of 100 random variables, distributed weibullly.

generate: function (n) { var randomVariables = []; for (var k = 0; k < n; k++ ) { randomVariables.push(-(1 / λ) * Math.log(mctad.getRandomArbitrary(0, 1))); } return randomVariables; }, pdf: function (x) { if (x >= 0) { return (k / λ) * Math.pow(x / λ, k - 1) * Math.pow(Math.E, -(Math.pow(x / λ, k))); } else { return 0.0; } }, cdf: function (x) { if (x >= 0) { return 1 - Math.pow(Math.E, -Math.pow(x / λ, k)); } else { return 0.0; } } };

Mix in the convenience methods for f(X) and F(X).

mctad.extend(dfs, mctad.continuousMixins); dfs.domain.max = Math.ceil(6 * dfs.variance); dfs.range.max = 0.1 * Math.ceil(10 * dfs.pdf(dfs.mode)); return dfs; };