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, , is written as
where and are called the primary and secondary distributions, respectively.
The compound distributions arise naturally as follows. Let N be a counting random variable with pgf . Let be i.i.d. counting random variables each with pgf . Assuming that the s do not depend on N, the pgf of the random sum (where implies ...