Random sums stopped by a rare event : a new approximation

• Autorzy: Gamboa F. , Pamphile P.
• Języki publikacji: EN

Abstrakty

EN

The convergence of a geometric sum of positive i.i.d. random variables to an exponential distribution is a well-known result. This convergence provided various and useful approximations in reliability, queueing or risk theory. However, for concrete applications, this exponential approximation is not sharp enough for small values of mission time. So, other approximations have been proposed (Bon and Pamphile (2001), Kalashnikov (1997)). In this paper we propose a new point of view where the exponential approximation appears as a first-order approximation. We consider more general random sums stopped by a rare event, where summands are no more assumed to be independent neither nonnegative. So we give a second-order approximation. As illustration we consider stopping time with negative binomial distribution. This approximation provides a new evaluation tool in reliability analysis of highly reliable systems. The accuracy of this approximation is studied numerically.

Słowa kluczowe

EN

random sums; limit theorems; approximations; reliability

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 2
• Strony: 237--252
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Gamboa F.

• University Paul Sabatier, Department of Probability and Statistics, 118 route de Narbonne, F-31062 Toulouse Cedex, France

autor

Pamphile P.

• University Paris Sud, Department of Mathematics, Bat 425, F-91405 Orsay Cedex, France

Bibliografia

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