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Convolutions of Distributions With Exponential and Subexponential Tails

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  09 April 2009

Daren B. H. Cline
Daren B. H. Cline
Affiliation:
Department of StatisticsTexas A & M UniversityCollege Station, Texas 77843, U.S.A.
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Distribution tails F(t) = F(t, ∞) are considered for which and as t → ∞. A real analytic proof is obtained of a theorem by Chover, Wainger and Ney, namely that .

In doing so, a technique is introduced which provides many other results with a minimum of analysis. One such result strengthens and generalizes the various known results on distribution tails of random sums.

Additionally, the closure and factorization properties for subexponential distributions are investigated further and extended to distributions with exponential tails.

Keywords

convolution tailsexponential tailssubexponential tails.

MSC classification

Secondary: 60E05: Distributions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 347 - 365
Copyright
Copyright © Australian Mathematical Society 1987

References

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