Characterizations of the Proportional (Reversed) Hazard Model

Abstract

In this article, we provide two simple characterizations of the proportional (reversed) hazard class of distributions based on some conditional expectation and conditional variance. Since exponential, Weibull, generalized exponential, Rayleigh, Burr type X, and exponentiated Weibull belong to the proportional (reversed) hazard class of distributions, the present results will provide characterizations of all these special cases.

Key Words:

• Conditional expectation
• Conditional variance
• Recurrence relation
• Exponentiated Weibull distribution

Acknowledgments

Part of the work of Professor R. D. Gupta was supported by the grant from the Natural Sciences and Engineering Research Council. The authors would also like to thank the guest editor Professor R. C. Gupta for some valuable comments.