期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2018
卷号：80
期号：2
页码：342-355
DOI：10.1007/s13171-017-0115-5
语种：English
出版社：Indian Statistical Institute
摘要：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.
关键词：Characterization ; Erlang distribution ; Exponential distributions ; Gamma function ; Risk model
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