A Characterization of Exponential Distribution in Risk Model

Chin-Yuan Hu, Jheng-Ting Wang and Tsung-Lin Cheng ()
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Chin-Yuan Hu: National Changhua University of Education
Jheng-Ting Wang: National Changhua University of Education
Tsung-Lin Cheng: National Changhua University of Education

Sankhya A: The Indian Journal of Statistics, 2018, vol. 80, issue 2, No 8, 342-355

Abstract: 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.

Keywords: Characterization; Erlang distribution; Exponential distributions; Gamma function; Risk model; Primary: 62E10; Secondary: 60G50 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13171-017-0115-5

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