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Computing maximum likelihood estimates from type II doubly censored exponential data

Author

Listed:
  • Arturo J. fernández

    (Universidad de La Laguna)

  • José I. Bravo

    (Universidad de La Laguna)

  • Íñigo Fuentes

    (Universidad de La Laguna)

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.

Suggested Citation

  • Arturo J. fernández & José I. Bravo & Íñigo Fuentes, 2002. "Computing maximum likelihood estimates from type II doubly censored exponential data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(2), pages 187-200, June.
    • Handle: RePEc:spr:stmapp:v:11:y:2002:i:2:d:10.1007_bf02511486
    DOI: 10.1007/BF02511486
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    References listed on IDEAS

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    1. Elfessi, Abdulaziz, 1997. "Estimation of a linear function of the parameters of an exponential distribution from doubly censored samples," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 251-259, December.
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    Cited by:

    1. Fernández, Arturo J., 2008. "Reliability inference and sample-size determination under double censoring for some two-parameter models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3426-3440, March.
    2. Carlos Pérez-González & Arturo Fernández, 2009. "Accuracy of approximate progressively censored reliability sampling plans for exponential models," Statistical Papers, Springer, vol. 50(1), pages 161-170, January.
    3. Fernandez, Arturo J., 2006. "Bayesian estimation based on trimmed samples from Pareto populations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1119-1130, November.
    4. Fernandez, Arturo J., 2006. "Bounding maximum likelihood estimates based on incomplete ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2014-2027, April.
    5. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    6. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.

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