Uniform distribution (discrete)

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In probability theory and statistics, the discrete uniform distribution is a discrete probability distribution that can be characterized by saying that all values of a finite set of possible values are equally probable.

A random variable that has any of [n] possible values [k_1,k_2,\dots,k_n] that are equally probable, has a discrete uniform distribution, then the probability of any outcome [k_i]  is [1/n]. A simple example of the discrete uniform distribution is throwing a fair dice. The possible values of [k] are 1, 2, 3, 4, 5, 6; and each time the dice is thrown, the probability of a given score is 1/6.

In case the values of a random variable with a discrete uniform distribution are real, it is possible to express the cumulative distribution function in terms of the degenerate distribution; thus

[F(k;a,b,n)=\sum_^n H(k-k_i)]

where the Heaviside step function [H(x-x_0)] is the CDF of the degenerate distribution centered at [x_0]. This assumes that consistent conventions are used at the transition points.

See rencontres numbers for an account of the probability distribution of the number of fixed points of a uniformly distributed random permutation.

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Miscellaneous:	Cantor • conditional • exponential family • infinitely divisible • location-scale family • marginal • maximum entropy • phase-type • posterior • prior • quasi • sampling

 

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