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Classes of life distributions and renewal counting process

Part of: Distribution theory Special processes

Published online by Cambridge University Press:  14 July 2016

Yi-Hau Chen
Yi-Hau Chen*
Affiliation:
National Taiwan University
*
∗Postal address: National Taiwan University, College of Public Health, Graduate Institute of Public Health, Division of Biostatistics, No. 1 Jen-Ai Road Sec. 1, Taipei, Taiwan, ROC.
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Abstract

We prove that if the renewal function M(t) corresponding to a life distribution F is convex (concave) then F is NBU (NWU), and hence answer two questions posed by Shaked and Zhu (1992). Moreover, based-on the renewal function, some characterizations of the exponential distribution within certain classes of life distributions are given.

Keywords

EXPONENTIAL DISTRIBUTIONRENEWAL COUNTING PROCESSDFRNBUNWUNBUENWUE

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1110 - 1115
Copyright
Copyright © Applied Probability Trust 1994 

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References

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