Some estimates of geometric sums
AbstractThe paper is devoted to analysis of geometric convolutions emerging in various fields of applied probability and, in particular, in reliability. The problem of bounding the distribution of such sums has been the subject of numerous works for last 20 years. Various bounds were proposed but their accuracy was sometimes not satisfactory for applications to highly reliable systems especially in the case of relatively small values of the time argument. Using truncation arguments, we propose new two-sided inequalities improving some known bounds.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 55 (2001)
Issue (Month): 1 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
- Cai, Jun & Willmot, Gordon E., 2005. "Monotonicity and aging properties of random sums," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 381-392, July.
- Mercier, Sophie, 2007. "Discrete random bounds for general random variables and applications to reliability," European Journal of Operational Research, Elsevier, vol. 177(1), pages 378-405, February.
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