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Some properties of ageing notions based on the moment-generating-function order

Part of: Special processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Xiaohu Li
Xiaohu Li*
Affiliation:
Lanzhou University
*
∗ Postal address: Department of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China. Email address: xhli@lzu.edu.cn
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Abstract

Classes of life distributions based on the moment-generating-function order are investigated in this paper. It is shown firstly that the class ℳ is closed under both convex linear combination and geometric compounding. Secondly, the class NBUmg (new better than used in the moment-generating-function order) is proved to be closed under increasing star-shaped transformations. Finally, the interplay between the stochastic comparison of the excess lifetime of a renewal process and the NBUmg interarrivals is studied.

Keywords

Convex linear combinationconvolutiongeometric compoundingℳ0-classℳ-classNBUmgstar-shaped transform

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 927 - 934
Copyright
Copyright © Applied Probability Trust 2004 

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