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A Characterization of Exponential Distribution in Risk Model

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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)

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.

Suggested Citation

  • Chin-Yuan Hu & Jheng-Ting Wang & Tsung-Lin Cheng, 2018. "A Characterization of Exponential Distribution in Risk Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 342-355, August.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:2:d:10.1007_s13171-017-0115-5
    DOI: 10.1007/s13171-017-0115-5
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    References listed on IDEAS

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    1. Gordon E. Willmot & X. Sheldon Lin, 2011. "Risk modelling with the mixed Erlang distribution," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 27(1), pages 2-16, January.
    2. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    3. Psarrakos, Georgios, 2010. "On the DFR property of the compound geometric distribution with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 428-433, December.
    4. Chin-Yuan Hu & Gwo Lin, 2003. "Characterizations of the exponential distribution by stochastic ordering properties of the geometric compound," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 499-506, September.
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