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

Uraiwan  Jaroengeratikun; Winai  Bodhisuwan; Ampai  Thongteeraparp

doi:10.4236/ojs.2012.22020

Uraiwan Jaroengeratikun, Winai Bodhisuwan, Ampai Thongteeraparp

Abstract: 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).

Keywords: Estimating Function; Zero Mean Martingale; Non-Life Insurance Claim Counting Process; Non-Homogeneous Poisson Process; Bell-Shaped Intensity; Beta-Shaped Intensity

Cite this paper: U. Jaroengeratikun, W. Bodhisuwan and A. Thongteeraparp, "A Bayesian Inference of Non-Life Insurance Based on Claim Counting Process with Periodic Claim Intensity," Open Journal of Statistics, Vol. 2 No. 2, 2012, pp. 177-183. doi: 10.4236/ojs.2012.22020.

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