A Statistical Analysis of Intensities Estimation on the Modeling of Non-Life Insurance Claim Counting Process
Uraiwan Jaroengeratikun, Winai Bodhisuwan, Ampai Thongteeraparp
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DOI: 10.4236/am.2012.31016   PDF   HTML     4,144 Downloads   8,684 Views   Citations

Abstract

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.

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U. Jaroengeratikun, W. Bodhisuwan and A. Thongteeraparp, "A Statistical Analysis of Intensities Estimation on the Modeling of Non-Life Insurance Claim Counting Process," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 100-106. doi: 10.4236/am.2012.31016.

Conflicts of Interest

The authors declare no conflicts of interest.

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