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Y. Lu and J. Garrido, “On Double Periodic Non-Homogeneous Poisson Processes,” Bulletin of the Swiss Association of Actuaries Swiss Association of Actuaries-Bern, Bern, 2004, pp. 195-212.

has been cited by the following article:

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

  AUTHORS: Uraiwan Jaroengeratikun, Winai Bodhisuwan, Ampai Thongteeraparp

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

  JOURNAL NAME: Applied Mathematics, Vol.3 No.1, January 4, 2012

  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.