Articlebronze1987

Convolutions of Distributions With Exponential and Subexponential Tails

150 citations0/0 files storedJournal of the Australian Mathematical Society Series A Pure Mathematics and Statistics

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Probability and Risk Models Probability and Statistical Research Statistical Distribution Estimation and Applications

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.

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References

1979Subexponentiality and infinite divisibility 1985Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities 1980On closure and factorization properties of subexponential and related distributions 1986Convolution tails, product tails and domains of attraction

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