, Volume 50, Issue 3, pp 211–220 | Cite as

On maximum likelihood prediction based on Type II doubly censored exponential data

  • Arturo J. Fernández


In this paper, the maximum likelihood predictor (MLP) of the kth ordered observation, t k, in a sample of size n from a two-parameter exponential distribution as well as the predictive maximum likelihood estimators (PMLE's) of the location and scale parameters, θ and β, based on the observed values t r, …, t s (1≤rs<kn), are obtained in closed forms, contrary to the belief they cannot be so expressed. When θ is known, however, the PMLE of β and MLP of t k do not admit explicit expressions. It is shown here that they exist and are unique; sharp lower and upper bounds are also provided. The derived predictors and estimators are reasonable and also have good asymptotic properties. As applications, the total duration time in a life test and the failure time of a k-out-of-n system may be predicted. Finally, an illustrative example is included.

Key words: Predictive likelihood Type II double censoring two-parameter exponential distribution order statistics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Arturo J. Fernández
    • 1
  1. 1.Departamento de Estadı´stica, I. O. y Computación, Facultad de Matemáticas, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain (e-mail:

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