J Austral Math Soc Ser A 43 pp347--365, 1987.

Convolutions of Distributions with Exponential and Subexponential Tails

Daren B. H. Cline

Abstract

Distribution tails¾F(t) = F(t, ¥) are considered for which¾F(t - u) - e^auF(t) and

F * F   (t) - 2d _ F   (t)

as t ® ¥. A real analytic proof is obtained of a theorem by Chover, Waigner and Ney, namely that

d = ó õ eauF(du).

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.

1980 AMS Subject Classification: 60E05

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Authors

Daren B. H. Cline

Department of Statistics, Texas A & M University, College Station, Texas 77843, U.S.A.