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

@article{Boyles1985InconsistencyOT,
  title={Inconsistency of the Maximum Likelihood Estimator of a Distribution Having Increasing Failure Rate Average},
  author={Russell A. Boyles and A. W. Marshall and Frank Proschan},
  journal={Annals of Statistics},
  year={1985},
  volume={13},
  pages={413-417}
}
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… 

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