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

• 作者: Ampai Thongteeraparp Uraiwan Jaroengeratikun Winai Bodhisuwan
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Estimating Function Zero Mean MARTINGALE NON-LIFE Insurance CLAIM Counting PROCESS Poisson PROCESS Bell-Shaped Intensity
• 年，卷（期）: yysxyw_2012,（1）
• 页码范围: 100-106
• 页数: 7页
• 分类号: O1

摘要

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.