Tweedie compound Poisson model with first order autoregressive time random effect

Abstract

Modeling with the Tweedie compound Poisson distribution is mostly done based on the Generalized Linear Model (GLM). GLM can be expanded into the Generalized Linear Mixed Model (GLMM) if there are fixed effects and random effects. GLMM modeling with Tweedie compound Poisson response variables is still rarely done because it is not analytically tractable and the density function cannot be stated in closed-form. By using the h-likelihood method, GLMM modeling with Tweedie compound Poisson can be solved numerically. This research models the Tweedie compound Poisson response variable by using GLMM with two random effects, region and the time assumed to follow the first-order autoregressive process. A simulation study is carried out with an evaluation using the average relative bias and the average MSE. The simulation results show the greater the autoregressive coefficient results in the smaller value of the relative bias. MSE values that are close to zero indicate the model is very good in describing data. An application, which is conducted to model the total number of claims in a certain area and time based on the 2014 profile of risk and loss of motor vehicle insurance in Indonesia, shows model has small value of absolute bias and MSE.