The Annals of Statistics

Inconsistency of the Maximum Likelihood Estimator of a Distribution Having Increasing Failure Rate Average

R. A. Boyles, A. W. Marshall, and F. Proschan

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 413-417.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346602

Digital Object Identifier
doi:10.1214/aos/1176346602

Mathematical Reviews number (MathSciNet)
MR773177

Zentralblatt MATH identifier
0605.62036

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62N05: Reliability and life testing [See also 90B25]

Keywords
Maximum likelihood estimation increasing failure rate average inconsistency

Citation

Boyles, R. A.; Marshall, A. W.; Proschan, F. Inconsistency of the Maximum Likelihood Estimator of a Distribution Having Increasing Failure Rate Average. Ann. Statist. 13 (1985), no. 1, 413--417. doi:10.1214/aos/1176346602. https://projecteuclid.org/euclid.aos/1176346602


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