Some Characterization Results Based on Factorization of the (Reversed) Hazard Rate Function

Abstract

In this article, the Fisher information is expressed in terms of the (reversed) hazard rate and several illustrated examples are given for its advantage. The concept is explored in the case of Type I and Type II censoring and characterization results are obtained for a class of distributions in which the (reversed) hazard rate factorizes into a function of the observation and a function of the parameter. Also, the Fisher information in the weighted models is studied with special emphasis on the exponential family of distributions. Finally, some concluding remarks are provided which help the practitioner to choose between the proposed procedure and the existing procedures.

Key Words:

• Characterization
• Exponential family
• Fisher information
• Information lack-of-memory; (Reversed) Hazard rate
• Type I and Type II censoring
• Weighted models

Mathematics Subject Classification:

• 62E10
• 62N01

Acknowledgments

The authors would like to thank the referee for some helpful suggestions. Part of the work of the first author was supported by a grant from the Natural Sciences and Engineering Research Council. The second author was supported by a travel grant from the Canadian American Center of the University of Maine.