JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol.80, no.5, pp.479-487, 2010 (SCI-Expanded)
The geometric Poisson (also called Polya-Aeppli) distribution is a particular case of the compound Poisson distribution. In this study, the explicit probability function of the geometric Poisson distribution is derived and a straightforward proof for this function is given. By means of a proposed algorithm, some numerical examples and an application on traffic accidents are also given to illustrate the usage of the probability function and proposed algorithm.