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THE SUBEXPONENTIAL PRODUCT CONVOLUTION OF TWO WEIBULL-TYPE DISTRIBUTIONS

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  18 May 2010

YAN LIU  and
QIHE TANG
YAN LIU
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, PR China (email: yanliu@whu.edu.cn)
QIHE TANG*
Affiliation:
Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA (email: qtang@stat.uiowa.edu)
*
✉For correspondence; e-mail: qtang@stat.uiowa.edu
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Abstract

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Let X1 and X2 be two independent and nonnegative random variables with distributions F1 and F2, respectively. This paper proves that if both F1 and F2 are of Weibull type and fulfill certain easily verifiable conditions, then the distribution of the product X1X2, called the product convolution of F1 and F2, belongs to the class 𝒮* and, hence, is subexponential.

Keywords

asymptoticsclass 𝒮*product convolutionWeibull-type distribution

MSC classification

Secondary: 60E05: Distributions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 2 , October 2010 , pp. 277 - 288
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This work was partially supported by the National Natural Science Foundation of China (No. 10971157 and No. 70871104), the Ministry of Education of China (No. 20070486093), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars.

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