High Quality Content by WIKIPEDIA articles! In probability theory, a compound Poisson distribution is the probability distribution of the sum of a "Poisson-distributed number" of independent identically-distributed random variables. In the simplest cases, the result can be either a continuous or a discrete distribution. Suppose that N is a random variable whose distribution is a Poisson distribution with expected value , and that are identically distributed random variables that are mutually independent and also independent of N. Then the probability distribution of the sum of N i.i.d. random variables conditioned on the number of these variables (N) is a well-defined distribution. In the case N = 0, then the value of Y is 0, so that then Y | N=0 has a degenerate distribution. The compound Poisson distribution is obtained by marginalising the joint distribution of (Y,N) over N, where this joint distribution is obtained by combining the conditional distribution Y | N with the marginal distribution of N.

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