Computing maximum likelihood estimates from type II doubly censored exponential data

Arturo J. Fernández (), José I. Bravo and Íñigo Fuentes
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Arturo J. Fernández: Universidad de La Laguna
José I. Bravo: Universidad de La Laguna
Íñigo Fuentes: Universidad de La Laguna

Statistical Methods & Applications, 2002, vol. 11, issue 2, No 5, 187-200

Abstract: 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.

Keywords: Maximum likelihood estimation; Type II double censoring; exponential distributions; order statistics; Bayes estimators (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/BF02511486

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