A characterization of exponential distribution in risk model

Chin Yuan Hu; Jheng Tinng Wang; Tsung-Lin Cheng

A characterization of exponential distribution in risk model

Chin Yuan Hu, Jheng Tinng Wang, Tsung-Lin Cheng

Graduate Institute of Statistics and Information Science

Research output: Contribution to journal › Article › peer-review

Abstract

In the general risk model (or the Sparre-Andersen model), it is well-known that the following assertion holds: If the claim size is exponentially distributed then the non-ruin probability distribution is a mixture of exponential distributions. In this paper, under some general conditions, we prove that the converse statement of the previous assertion is also true. Besides, we define a new non-ruin measure associated with the aggregate logarithms of the claim-over-profit ratios and obtain a result on Pareto-type distributions.

Original language	English
Pages (from-to)	342-355
Number of pages	14
Journal	Sankhya: The Indian Journal of Statistics
Volume	80
Publication status	Published - 2018 Jan 1

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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AB - In the general risk model (or the Sparre-Andersen model), it is well-known that the following assertion holds: If the claim size is exponentially distributed then the non-ruin probability distribution is a mixture of exponential distributions. In this paper, under some general conditions, we prove that the converse statement of the previous assertion is also true. Besides, we define a new non-ruin measure associated with the aggregate logarithms of the claim-over-profit ratios and obtain a result on Pareto-type distributions.

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