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On the DFR property of the compound geometric distribution with applications in risk theory

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  • Psarrakos, Georgios

Abstract

In 1988, Shanthikumar proved that the sum of a geometrically distributed number of i.i.d. DFR random variables is also DFR. In this paper, motivated by the inverse problem, we study monotonicity properties related to defective renewal equations, and obtain that if a compound geometric distribution is DFR, then the random variables of the sums are NWU (a class that contains DFR). Furthermore, we investigate some applications of risk theory and give a characterization of the exponential distribution.

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  • 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.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:428-433
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    References listed on IDEAS

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    1. David Dickson, 1998. "On a Class of Renewal Risk Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 60-68.
    2. Bhattacharjee, Manish C. & Ravi, S. & Vasudeva, R. & Mohan, N. R., 2003. "New order preserving properties of geometric compounds," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 113-120, August.
    3. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    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.
    5. Willmot, Gordon E., 2002. "Compound geometric residual lifetime distributions and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 421-438, June.
    6. 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.
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    Cited by:

    1. 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.

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