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


Cakmakyapan S. , Ozel G.

11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Greece, 21 - 27 September 2013, vol.1558, pp.1446-1449 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1558
  • Doi Number: 10.1063/1.4825790
  • Country: Greece
  • Page Numbers: pp.1446-1449

Abstract

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.