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# Discrete Distributions

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# Discrete Distributions

A discrete distribution is comprised of a set of probability values, P(xi), for discrete entities, xi, i=1,2...,N such that ΣP(xi)=1. A simple example is the discrete Uniform distribution over integers in the range [1,N]. In this case there are N separate entities, 1,2,3,4,...N, and each has the same probability of occurrence, P(xi)=1/N. A generalized discrete distribution consists of a similar set of probability values, typically ordered on and directly mappable to the Integers, but with varying probabilities. For example, the set of discrete values {0,1,2,3,4} could have associated discrete probabilities {0.15,0.20,0.30,0.20,0.15}. The sum of these probabilities is 1, as is required, and the mean is obtained in the usual manner, as: hence in this example, the mean = 2.

The following are examples of well-known discrete probability distributions, each of which is described in further detail in the subsections below: Binomial, Negative Binomial (Pascal),Hypergeometric, Multinomial, Poisson, Skellam and Zipf .