Aging and other distributional properties of discrete compound geometric distributions

Insurance: Mathematics and Economics

Volumn 28, Issue 3, 2001, Pages 361-379

  Willmot, Gordon E ^a,b   Cai, Jun ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF TORONTO   (Canada)

^c UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Best exponential upper bound; Discrete compound geometric distribution; Discrete decreasing failure rate; Discrete increasing mean residual lifetime; Discrete log convex; Discrete strongly new worse than used; M G 1 queue length; Mixed Poisson distribution

Indexed keywords

EID: 0037758216     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(01)00062-2     Document Type: Article

References (26)

1. Asmussen, S., 1987. Applied Probability and Queues. Wiley, Chichester, UK.
2. Barlow, R., Proschan, F., 1965. Mathematical Theory of Reliability. Wiley, New York.
3. Brown M. Error bounds for exponential approximations of geometric convolutions. Annals of Probability. 18:1990;1388-1402.
4. Cai J., Garrido J. A unified approach to the study of tail probabilities of compound distributions. Journal of Applied Probability. 36:1999;1058-1073.
5. Cai J., Kalashnikov V. NWU property of a class of random sums. Journal of Applied Probability. 37:2000;283-289.
6. Fagiuoli E., Pellerey F. Preservation of certain classes of life distributions under Poisson shock models. Journal of Applied Probability. 31:1994;458-465.
7. Feller, W., 1968. An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Edition. Wiley, New York.
8. Gerber H. Mathematical fun with ruin theory. Insurance: Mathematics and Economics. 7:1988;15-23.
9. Gertsbakh I. Asymptotic methods in reliability: a review. Advances in Applied Probability. 6:1984;147-175.
10. Grandell, J., 1997. Mixed Poisson Processes. Chapman & Hall, London.
11. Klefsjö B. HNBUE survival under some shock models. Scandinavian Journal of Statistics. 8:1981;39-47.
12. Klefsjö B. The HNBUE and HNWUE classes of life distributions. Naval Research Logistics Quarterly. 29:1982;331-344.
13. Klefsjö B. A useful aging property based on the Laplace transform. Journal of Applied Probability. 20:1983;615-625.
14. Klugman, S., Panjer, H., Willmot, G., 1998. Loss Models: From Data to Decisions. Wiley, New York.
15. Lin X. Tail of compound distributions and excess time. Journal of Applied Probability. 33:1996;184-195.
16. Pellerey F., Shaked M., Zinn J. Nonhomogeneous Poisson processes and logconcavity. Probability in the Engineering and Informational Sciences. 14:2000;353-373.
17. Rolski, T., Schmidli, H., Schmidt, V., Teugels, J., 1999. Stochastic Processes for Insurance and Finance. Wiley, Chichester, UK.
18. Ross, S., 1996. Stochastic Processes. Wiley, New York.
19. Shanthikumar J.G. DFR property of first passage times and its preservation under geometric compounding. Annals of Probability. 16:1988;397-406.
20. Shiu E. The probability of eventual ruin in the compound binomial model. ASTIN Bulletin. 19:1989;179-190.
21. Steutel, F., 1970. Preservation of infinite divisibility under mixing and related topics. Math. Centre Tracts 33. Math. Centre, Amsterdam.
22. Van Harn, K., 1978. Classifying infinitely divisible distributions by functional equations. Math. Centre Tracts 103. Math. Centre, Amsterdam.
23. Willmot G. Ruin probabilities in the compound binomial model. Insurance: Mathematics and Economics. 12:1993;133-142.
24. Willmot G. Refinements and distributional generalizations of Lundberg's inequality. Insurance: Mathematics and Economics. 15:1994;49-63.
25. Willmot G., Cai J. On classes of lifetime distributions with unknown age. Probability in the Engineering and Informational Sciences. 14:2000;473-484.
26. Willmot, G., Lin, X., 1994. Lundberg bounds on the tails of compound distributions. Journal of Applied Probability 31, 743-756.