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 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
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A characterization of exponential distribution in risk model. / Hu, Chin Yuan; Wang, Jheng Tinng; Cheng, Tsung-Lin.
In: Sankhya: The Indian Journal of Statistics, Vol. 80, 01.01.2018, p. 342-355.Research output: Contribution to journal › Article
TY - JOUR
T1 - A characterization of exponential distribution in risk model
AU - Hu, Chin Yuan
AU - Wang, Jheng Tinng
AU - Cheng, Tsung-Lin
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85069487989&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85069487989&partnerID=8YFLogxK
M3 - Article
VL - 80
SP - 342
EP - 355
JO - Sankhya: The Indian Journal of Statistics
JF - Sankhya: The Indian Journal of Statistics
SN - 0972-7671
ER -