Uniform Distribution (Continuous)

The Continuous Uniform Distribution or Rectangular Distribution is a family of symmetric, continuous probability distributions such that for each member of the family, all intervals of the same length on the distribution are equally probable.

Assumptions

a and b are real numbers, the minimum and maximum values, with a < b; a may be thought of as a location parameter, (b - a) as a scale parameter.

Use

mctad.uniform(a, b)

Inline Comments

mctad.uniform = function (a, b) {

Check that a < b.

if (a >= b) { return undefined; } var dfs = { mean: (a + b) / 2, median: (a + b) / 2, mode: undefined, // not clear what to return, as any value in [a, b] is modal variance: Math.pow(b - a, 2) / 12, skewness: 0, entropy: Math.log(b - a), domain: { min: a, max: b }, range: { min: 0, max: Infinity },

mctad.uniform(10, 20).generate(100) will generate an Array of 100 random variables, distributed uniformly between 10 and 20, inclusive.

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

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

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