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March, 1985 Inconsistency of the Maximum Likelihood Estimator of a Distribution Having Increasing Failure Rate Average
R. A. Boyles, A. W. Marshall, F. Proschan
Ann. Statist. 13(1): 413-417 (March, 1985). DOI: 10.1214/aos/1176346602

Abstract

Marshall and Proschan (1965) showed that the MLE for a life distribution with increasing failure rate is strongly consistent. In this note we show that the MLE for a life distribution with increasing failure rate average is not consistent; in fact, maximum likelihood estimation in the IFRA case yields estimators of the average failure rate and of the distribution function which, in general, converge a.s. to values other than the true values. In the decreasing failure rate average case, the MLE fails to exist.

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R. A. Boyles. A. W. Marshall. F. Proschan. "Inconsistency of the Maximum Likelihood Estimator of a Distribution Having Increasing Failure Rate Average." Ann. Statist. 13 (1) 413 - 417, March, 1985. https://doi.org/10.1214/aos/1176346602

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0605.62036
MathSciNet: MR773177
Digital Object Identifier: 10.1214/aos/1176346602

Subjects:
Primary: 62G05
Secondary: 62N05

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 1 • March, 1985
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