Convolutions of Distributions With Exponential and Subexponential Tails

Abstract

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.