Uniform Distribution (Discrete)

The Discrete Uniform Distribution is a symmetric probability distribution where a finite number of values are equally likely to be observed. A common example of its application is the roll of a fair die, where the equally likely outcomes 1, 2, …, 6 each have probability 1/6.

Assumptions

i and j are Integers, the lower and upper bounds of a range of equally likely Integers.

Use

mctad.discreteUniform(i, j)

Inline Comments

mctad.discreteUniform = function (i, j) {

Check that i ≤ j, and that i and j are integers.

if (i > j || !mctad.isInteger(i) || !mctad.isInteger(j) ) { return undefined; } var x, pmf, cdf = 0, dfs = { mean: (i + j)/2, median: (i + j)/2, mode: undefined, variance: (Math.pow((j - i + 1), 2) - 1)/12, skewness: 0.0, entropy: Math.log(j - i + 1), domain: { min: i, max: j }, range: { min: 0.0, max: 0.0 },

mctad.discreteUniform(1, 6).generate(10) will generate an Array of 10 random variables, distributed uniformly between 1 and 6, inclusive, as in the roll of a fair die.

generate: function (n) { var randomVariables = []; for (var k = 0; k < n; k++ ) { randomVariables.push(mctad.getRandomInt(i, j)); } return randomVariables; } };

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

for (x = i; x <= j; x++) { pmf = 1/(j - i + 1); cdf += pmf; dfs[x] = { pmf: pmf, cdf: cdf }; if (pmf > dfs.range.max) { dfs.range.max = 0.1 * Math.ceil(10 * pmf); } }

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

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