Statistik für bivariate gemischte poisson-prozesse am beispiel der kraftfahrthaftpflichtversicherung

In this paper we show that the model of the bivariate mixed Poisson process arises in a natural way from the univariate mixed Poisson process, which is used in several areas for counting certain events. Furthermore we state some properties of the bivariate process. In the second part of the paper we illustrate how by means of the bivariate mixed Poisson process a bonus-malus system handling different types of accidents can be derived from the classical bonus-malus system in third-party liability insurance. To this end we first check the model on the given data and then estimate distribution parameters and compute net premiums for different mixing distributions as well as test the prediction probabilities. © Physica-Verlag 2005.