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Proofs of the closure property of NBUC and NBU(2) under convolution

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Taizhong Hu  and
Huiliang Xie
Taizhong Hu*
Affiliation:
University of Science and Technology of China
Huiliang Xie*
Affiliation:
University of Science and Technology of China
*
∗ Postal address: Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
∗ Postal address: Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
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Abstract

In this note, we give new proofs of the closure property of ageing classes NBUC and NBU(2) under convolution to make up the gaps in the proofs of Cao and Wang (1991) and of Li and Kochar (2001).

Keywords

Ageing classesNBUCNBU(2)convolution

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 224 - 227
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Supported by NSFC (Grant No. 10171093), the National 973 Fundamental Research Program on Financial Engineering (Grant No. G1998030418), and a grant of the Chinese Academy of Sciences.

References

Barlow, R. E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Block, H. W., and Savits, T. H. (1976). The IFRA closure problem. Ann. Prob. 4, 1030–1032.Google Scholar
Cao, J., and Wang, Y. (1991). The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479. (Correction: J. Appl. Prob. 29 (1992), 753.)Google Scholar
Li, X., and Kochar, S. C. (2001). Some new results involving the NBU(2) class of life distributions. J. Appl. Prob. 38, 242–247.Google Scholar