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Tail of compound distributions and excess time

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Xiaodong Lin
Xiaodong Lin*
Affiliation:
University of Toronto
*
∗Postal address: Department of Statistics, University of Toronto, Toronto, Ontario M5S 1A1, Canada.
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Abstract

Bounds on the tail of compound distributions are considered. Using a generalization of Wald's fundamental identity, we derive upper and lower bounds for various compound distributions in terms of new worse than used (NWU) and new better than used (NBU) distributions respectively. Simple bounds are obtained when the claim size distribution is NWUC, NBUC, NWU, NBU, IMRL, DMRL, DFR and IFR. Examples on how to use these bounds are given.

Keywords

EXCESS TIMEEXPONENTIAL AND NON-EXPONENTIAL BOUNDSINSURANCE RISKNEW BETTER THAN USEDNEW WORSE THAN USEDRUIN PROBABILITYWALD'S IDENTITYM/G/1 QUEUE

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 184 - 195
Copyright
Copyright © Applied Probability Trust 1996 

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