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

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.

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.

Cite this paper

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.

U. Jaroengeratikun, W. Bodhisuwan and A. Thongteeraparp, "A Statistical Analysis of Intensities Estimation on the Modeling of Non-Life Insurance Claim Counting Process,"

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