Faculty Publications

Title

Some characterization of distributions by functions of failure rate and mean residual life

Document Type

Article

Keywords

Monotonicity, Residual moments, Uniqueness, Variance residual life

Journal/Book/Conference Title

Communications in Statistics - Theory and Methods

Volume

33

Issue

12

First Page

3115

Last Page

3131

Abstract

In reliability studies, it is well known that the failure rate, the mean residual life function, and their product characterize the distribution. In this article, we show that their ratio also characterizes the distribution, This result is then utilized to show that the second residual moment characterizes the distribution. A general uniqueness theorem is proved to show that the variance residual life function characterizes the distribution. An example is presented to illustrate the results. Finally, some applications, of the results established earlier, to nonhomogeneous Poisson processes are provided.

Original Publication Date

12-1-2004

DOI of published version

10.1081/STA-200039060

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