General Principles for Discrete Distributions

Abstract

A discrete random variable is a random variable taking only integer values. The distribution of a discrete random variable X is determined by its probability mass function (pmf), p _k = Prob(X = k). It is also called probability vector if its support is bounded from below. In the latter case we assume without loss of generality that X is only taking values on the nonnegative integers. We then write (p ₀, p ₁...) for the probability vector. To generate discrete random variates we can apply the inversion (Sect. 3.1) and the rejection principle (Sect. 3.3) that are also of major importance for continuous distributions. We also present the alias method (Sect. 3.2) which was developed especially for discrete distributions.