On The Expected Value and Distribution Function of The First Exit Time for The Polya-Aeppli Process

Polya-Aeppli process is a particular case of classical compound Poisson process where the contribution of each term is distributed according to the geometric distribution and is used for describing clustered data since the Poisson process is insufficient for clustering of events. In this study, the distribution function and expected value of the first exit time are derived forPolya-Aeppli process. Then, an application based on traffic accidents in Groningen are given and expectedtimes obtainedfor some time-independent boundaries using R project.