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Convolutions of Distributions With Exponential and Subexponential Tails
- Part of
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 43 / Issue 3 / December 1987
- Published online by Cambridge University Press:
- 09 April 2009, pp. 347-365
- Print publication:
- December 1987
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- Article
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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.
and 
as 
.