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Some new results on the subexponential class

Published online by Cambridge University Press:  14 July 2016

Emily S. Murphree
Emily S. Murphree*
Affiliation:
Miami University
*
∗ Postal address: Department of Mathematics and Statistics, Bachelor Hall, Miami University, Oxford, OH 45056, USA.
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Abstract

A distribution function F on (0,∞) belongs to the subexponential class if the ratio of 1 – F(2)(x) to 1 – F(x) converges to 2 as x →∞. A necessary condition for membership in is used to prove that a certain class of functions previously thought to be contained in has members outside of . Sufficient conditions on the tail of F are found which ensure F belongs to ; these conditions generalize previously published conditions.

Keywords

SUBEXPONENTIAL DISTRIBUTIONMODERATE GROWTHSLOW GROWTHRENEWAL THEORYBRANCHING PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 892 - 897
Copyright
Copyright © Applied Probability Trust 1989 

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