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Some estimates of geometric sums

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  • Bon, Jean-Louis
  • Kalashnikov, Vladimir

Abstract

The 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.

Suggested Citation

  • Bon, Jean-Louis & Kalashnikov, Vladimir, 2001. "Some estimates of geometric sums," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 89-97, November.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:1:p:89-97
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Cai, Jun & Willmot, Gordon E., 2005. "Monotonicity and aging properties of random sums," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 381-392, July.
    2. Chadjiconstantinidis, Stathis & Xenos, Panos, 2022. "Refinements of bounds for tails of compound distributions and ruin probabilities," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    3. Mathieu Emily & Pierre Casez & Olivier François, 2009. "Risk Assessment for Hospital‐Acquired Diseases: A Risk‐Theory Approach," Risk Analysis, John Wiley & Sons, vol. 29(4), pages 565-575, April.
    4. 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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