Inconsistency of Maximum Likelihood Estimator of Distributions Having Increasing Failure Rate Average,

Abstract

Marshall and Proschan showed that the MLE for a life distribution with increasing failure rate is strongly consistent (Ann. Math. Statist., 1965, 36, 69-77). In this note the author shows 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, coverage a.s. to values other than the true values. In the decreasing failure rate average case, the MLE fails to exist.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1975
Accession Number
ADA015911

Entities

People

  • A. W. Marshall
  • Frank Proschan

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • British Columbia
  • Cooperation
  • Distribution Functions
  • Estimators
  • Mathematics
  • Maximum Likelihood Estimation
  • Measurement Transportation Algorithms
  • Optimal Estimators
  • Statistical Algorithms

Readers

  • Statistical inference.