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Asymptotic tail behaviour of Poisson mixtures by applications

Published online by Cambridge University Press:  01 July 2016

Gordon E. Willmot
Gordon E. Willmot*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont., Canada, N2L 3G1.
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Abstract

This expository paper deals with the right tail behaviour of a class of Poisson mixtures. An Abelian-type result is obtained using basic theory of regular variation. Applications to compound distributions in insurance risk theory and queue length distributions under various queue disciplines in the case of Poisson arrivals are then discussed.

Keywords

REGULAR VARIATIONCOMPOUND DISTRIBUTIONSINSURANCE RISK THEORYM/G/1 QUEUE LENGTHFEEDBACK QUEUESQUEUES WITH VACATIONSQUEUES WITH WARM-UP TIMES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 147 - 159
Copyright
Copyright © Applied Probability Trust 1990 

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