%0 Journal Article
%T A Bayesian Inference of Non-Life Insurance Based on Claim Counting Process with Periodic Claim Intensity
%A Uraiwan Jaroengeratikun
%A Winai Bodhisuwan
%A Ampai Thongteeraparp
%J Open Journal of Statistics
%P 177-183
%@ 2161-7198
%D 2012
%I Scientific Research Publishing
%R 10.4236/ojs.2012.22020
%X 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,¦«(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 compensator¦«(t).
%K Estimating Function
%K Zero Mean Martingale
%K Non-Life Insurance Claim Counting Process
%K Non-Homogeneous Poisson Process
%K Bell-Shaped Intensity
%K Beta-Shaped Intensity
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=18596