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, 
, 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 ...
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