A Statistical Analysis of Intensities Estimation on the Modeling of Non-Life Insurance Claim Counting Process

This study presents an estimation approach to non-life insurance claim counts relating to a specified time. The objective of this study is to estimate the parameters in non-life insurance claim counting process, including the homogeneous Poisson process (HPP) and the non-homogeneous Poisson process (NHPP) with a bell-shaped intensity. We use the estimating function, the zero mean martingale (ZMM) as a procedure of parameter estimation in the insurance claim counting process. Then, Λ(t) , the compensator of is proposed for the number of claims in the time interval . We present situations through a simulation study of both processes on the time interval . Some examples of the situations in the simulation study are depicted by a sample path relating to its compensator Λ(t). In addition, an example of the claim counting process illustrates the result of the compensator estimate misspecification.

A Bayesian Inference of Non-Life Insurance Based on Claim Counting Process with Periodic Claim Intensity

The aim of this study is to propose an estimation approach to non-life insurance claim counts related to the insurance claim counting process, including the non-homogeneous Poisson process (NHPP) with a bell-shaped intensity and a beta-shaped intensity. The estimating function, such as the zero mean martingale (ZMM), is used as a procedure for parameter estimation of the insurance claim counting process, and the parameters of model claim intensity are estimated by the Bayesian method. Then,Λ(t), the compensator of N(t) is proposed for the number of claims in a time interval (0,t]. Given the process over the time interval (0,t]., the situations are presented through a simulation study and some examples of these situations are also depicted by a sample path relating N(t) to its compensatorΛ(t).