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December, 1975 The Class of Subexponential Distributions
Jozef L. Teugels
Ann. Probab. 3(6): 1000-1011 (December, 1975). DOI: 10.1214/aop/1176996225

Abstract

The class $\mathscr{J}$ of subexponential distributions is characterized by $F(0) = 0, 1 - F^{(2)} (x) \sim 2\{1 - F(x)\}$ as $x \rightarrow \infty$. New properties of the class $\mathscr{J}$ are derived as well as for the more general case where $1 - F^{(2)} (x) \sim \beta\{1 - F(x)\}$. An application to transient renewal theory illustrates these results as does an adaptation of a result of Greenwood on randomly stopped sums of subexponentially distributed random variables.

Citation

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Jozef L. Teugels. "The Class of Subexponential Distributions." Ann. Probab. 3 (6) 1000 - 1011, December, 1975. https://doi.org/10.1214/aop/1176996225

Information

Published: December, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0374.60022
MathSciNet: MR391222
Digital Object Identifier: 10.1214/aop/1176996225

Subjects:
Primary: 60E05
Secondary: 60G40

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 6 • December, 1975
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