Genel Etkili Homojen Poısson Süreçlerine Dayanan Bağımlı Birleşik Poısson Süreçleri

Abstract

A common shock Poisson process is used to model dependent event frequencies. In this process, a shock may be a big car accident, a particular hurricane, a medical mistake with consequences in a hospital. The common shock Poisson process allows for detailed and separate specification of dependence in frequency. However, common shock has never been used to model dependency between compound Poisson processes in detail.In this study, firstly, independent compound Poisson processes with common shock are defined and some characteristics of these processes are obtained. The sum of independent compound Poisson processes with common shock is investigated. Then, the dependent compound Poisson processes based on common shock are proposed and their joint probability function is obtained. The sum of dependent compound Poisson processes with common shock models is also derived. Finally, to show the applicability of our findings an application based on the forest fires in Turkey are provided.