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Sharp reliability bounds for the ℒ-like distributions, a class in which ageing is based on Laplace transform inequalities

Part of: Distribution theory - Probability Integral transforms, operational calculus Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Chin-Yuan Hu  and
Gwo Dong Lin
Chin-Yuan Hu*
Affiliation:
National Changhua University of Education
Gwo Dong Lin*
Affiliation:
Academia Sinica, Taiwan
*
∗Postal address: Department of Business Education, National Changhua University of Education, Changhua, 50058, Taiwan, Republic of China. Email address: buhuua@cc.ncue.edu.tw
∗∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 11529, Taiwan, Republic of China. Email address: gdlin@stat.sinica.edu.tw
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Abstract

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We establish Klar's (2002) conjecture about sharp reliability bounds for life distributions in the ℒα-class in reliability theory. The key idea is to construct a set of two-point distributions whose support points satisfy a certain system of equalities and inequalities.

Keywords

ℒ-classℒα-classreliability bound

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 44A10: Laplace transform 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1204 - 1208
Copyright
© Applied Probability Trust 2005 

References

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Klefsjö, B. (1983). A useful ageing property based on the Laplace transform. J. Appl. Prob. 20, 615–626.Google Scholar
Lin, G. D. (1998). On weak convergence within the { ℒ-like classes of life distributions. Sankhyā A 60, 176–183.Google Scholar
Lin, G. D. and Hu, C.-Y. (2000). A note on the { ℒ-class of life distributions. Sankhyā A 62, 267–272.Google Scholar
Mohan, N. R. and Ravi, S. (2002). Some properties of two families of classes of life distributions. J. Appl. Prob. 39, 581–589.Google Scholar
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