Applications
A compound Poisson distribution, in which the summands have an exponential distribution, was used by Revfeim to model the distribution of the total rainfall in a day, where each day contains a Poisson-distributed number of events each of which provides an amount of rainfall which has an exponential distribution. Thompson applied the same model to monthly total rainfalls.
The discrete compound Poisson distribution is also widely used in actuarial science and insurance for modelling the distribution of the total claim amount of the sum of a random number of independent and identically distributed claim amounts X1, X2, ..., XN.
Read more about this topic: Compound Poisson Distribution