7Advanced Discrete Distributions

7.1 Compound Frequency Distributions

A larger class of distributions can be created by the processes of compounding any two discrete distributions. The term compounding reflects the idea that the pgf of the new distribution, img, is written as

where img and img are called the primary and secondary distributions, respectively.

The compound distributions arise naturally as follows. Let N be a counting random variable with pgf img. Let img be i.i.d. counting random variables each with pgf img. Assuming that the imgs do not depend on N, the pgf of the random sum img (where implies ...

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