The Neyman type A and B Processes, Thomas process and Polya-Aeppli process are used for describing clustered data since the Poisson process is insufficient for clustering of events. In this study, new probability functions and the distribution functions of first exit times are derived for these generalized Poisson processes. Then, an empirical comparison of the proposed probability functions and an application based on traffic accidents in Groningen are given via prepared program in Oracle database.