Normal Distribution

The Normal Distribution or Gaussian Distribution is a family of symmetric, continuous probability distributions.

Assumptions

μ and σ2 are real numbers, the mean and variance.

Use

mctad.normal(μ, σ2)

Inline Comments

mctad.normal = function (μ, σ2) {

Check that σ2 > 0.

if (σ2 <= 0) { return undefined; } var dfs = { mean: μ, median: μ, mode: μ, variance: σ2, skewness: 0, entropy: 0.5 * Math.log(2 * mctad.π * Math.E * σ2), domain: { min: -Infinity, max: Infinity }, range: { min: 0, max: Infinity },

mctad.normal(-2.0, 0.5).generate(100) will generate an Array of 100 random variables, distributed normally with mean -2 and variance 0.5. The implementation uses the Marsaglia Polar Method.

generate: function (n) { var U = [], V = [], W, Y, randomVariables = []; for (var k = 0; k < n / 2; k++ ) { do { U = [mctad.getRandomArbitrary(0, 1), mctad.getRandomArbitrary(0, 1)]; V = [2 * U[0] - 1, 2 * U[1] - 1]; W = Math.pow(V[0], 2) + Math.pow(V[1], 2); } while (W > 1); Y = Math.sqrt((-2 * Math.log(W) / W)); randomVariables.push(μ + Math.sqrt(σ2) * (V[0] * Y), μ + Math.sqrt(σ2) * (V[1] * Y)); } if (randomVariables.length === n + 1) { randomVariables.pop(); } return randomVariables; }, pdf: function (x) { return (1 / (Math.sqrt(σ2) * Math.sqrt(2 * mctad.π))) * Math.pow(Math.E, -(Math.pow(x - μ, 2) / (2 * σ2))); }, cdf: function (x) { var Z = (x - μ) / Math.sqrt(2 * σ2); if (Z >= 0) { return 0.5 * (1.0 + mctad.erf(Z)); } else { return 0.5 * (1.0 - mctad.erf(-Z)); } } };

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

mctad.extend(dfs, mctad.continuousMixins); dfs.domain.min = μ - Math.ceil(3 * dfs.variance); dfs.domain.max = μ + Math.ceil(3 * dfs.variance); dfs.range.max = 0.1 * Math.ceil(10 * dfs.pdf(μ)); return dfs; };