Statistical Methods

Statistical Methods and Applications

, Volume 11, Issue 2, pp 187-200

Computing maximum likelihood estimates from type II doubly censored exponential data

  • Arturo J. fernándezAffiliated withDepartamento de Estadística, I. O. y Computación, Facultad de Matemáticas, Universidad de La Laguna
  • , José I. BravoAffiliated withDepartamento de Estadística, I. O. y Computación, Facultad de Matemáticas, Universidad de La Laguna
  • , Íñigo De FuentesAffiliated withDepartamento de Estadística, I. O. y Computación, Facultad de Matemáticas, Universidad de La Laguna

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Abstract

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.

Key words

Maximum likelihood estimation Type II double censoring exponential distributions order statistics Bayes estimators