Thinning process algorithms for compound poisson process having nonhomogeneous poisson process (NHPP) intensity functions

Abstract

Abstract One stochastic process that is often used to model real phenomena is the compound Poisson process (CPP). CPP is a process in which a component in the process of the events occurred is assumed to be a Poisson process with a certain intensity function (homogeneous or nonhomogeneous). Thinning process algorithm is usually used to generate events that occurred in the Poisson process, but not yet in CPP. This study aims to find out the algorithm to produce CPP which has the function of Poisson nonhomogeneous (NHPP) intensity, where in addition to knowing the process of events that occur, it also takes into account the extent of the consequences of these events. The value of the load caused by the Poisson process is assumed to be a family of i.i.d random variables and the variables are also independent of the Poisson process. The results of this study have obtained the thinning process algorithm and its generalizations for compound Poisson process having nonhomogeneous Poisson process (NHPP) intensity functions. This algorithm is the result of theoretical development and analysis of computational simulations that can be applied in various fields of science such as the analysis of reliability and risk models.