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Convolutions of Distributions With Exponential and Subexponential Tails

Published online by Cambridge University Press:  09 April 2009

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.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

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