On maximum likelihood prediction based on Type II doubly censored exponential data |
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Authors: | Arturo J Fernández |
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Institution: | (1) Departamento de Estadı′stica, I. O. y Computación, Facultad de Matemáticas, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain (e-mail: ajfernan@ull.es), ES |
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Abstract: | 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≤r≤s<k≤n), 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.
Received: August 1999 |
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Keywords: | : Predictive likelihood Type II double censoring two-parameter exponential distribution order statistics |
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