Inconsistency of the maximum likelihood estimator of a distribution having increasing failure rate average
type: Item
instance of: scholarly article
title: Inconsistency of the maximum likelihood estimator of a distribution having increasing failure rate average
zbMATH Open document ID: 0605.62036
author: R. A. Boyles
author: Albert W. Marshall
author: Frank Proschan
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: The last two authors [Ann. Math. Stat. 36, 69-77 (1965; Zbl 0128.385)] 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.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 3978145
zbMATH Keywords: DFRA
zbMATH Keywords: inconsistency
zbMATH Keywords: MLE
zbMATH Keywords: life distribution
zbMATH Keywords: increasing failure rate
zbMATH Keywords: increasing failure rate average
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: IFRA
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346602
OpenAlex ID: W2071402202
DOI: 10.1214/AOS/1176346602
description: scientific article; zbMATH DE number 3978145