Exponential Distribution

The Exponential Distribution is the continuous analog of the [Geometric Distribution(../discrete/geometric.html); also, it describes the time between events in a Poisson process.

Assumptions

λ is a strictly positive real number, which represents the constant average rate at which events occur, continuously and independently.

Use

mctad.exponential(λ)

Inline Comments

mctad.exponential = function (λ) {

Check that λ > 0.

if (λ < 0) { return undefined; } var dfs = { mean: 1 / λ, median: (1 / λ) * Math.log(2), mode: 0.0, variance: Math.pow((1 / λ), 2), skewness: 2.0, entropy: 1 - Math.log(λ), domain: { min: 0, max: Infinity }, range: { min: 0, max: Infinity },

mctad.exponential(1.5).generate(100) will generate an Array of 100 random variables, distributed exponentially.

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 λ * Math.pow(Math.E, -λ * x); } else { return undefined; } }, cdf: function (x) { if (x >= 0) { return 1 - Math.pow(Math.E, -λ * x); } 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(4 * dfs.variance); dfs.range.max = 0.1 * Math.ceil(10 * dfs.pdf(0.0)); return dfs; };