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Continuous Mixtures of Exponentials and IFR Gammas Having Bathtub-Shaped Failure Rates

Part of: Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Naftali A. Langberg ,
Thomas H. Savits  and
Jie Wang
Henry W. Block*
Affiliation:
University of Pittsburgh
Naftali A. Langberg*
Affiliation:
University of Haifa
Thomas H. Savits*
Affiliation:
University of Pittsburgh
Jie Wang*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
∗∗∗∗Postal address: Department of Statistics, University of Haifa, Mount Carmel, Haifa 31999, Israel.
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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Abstract

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It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped failure rate.

Keywords

Reliabilityfailure rate functionbathtub failure rate

MSC classification

Secondary: 62N05: Reliability and life testing
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 4 , December 2010 , pp. 899 - 907
Copyright
Copyright © Applied Probability Trust 2010 

References

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