caa a22 4500 47579303X CHVBK 20180406123715.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/s001840050046 doi (NATIONALLICENCE)springer-10.1007/s001840050046 Fernández Arturo J. 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 aut On maximum likelihood prediction based on Type II doubly censored exponential data [Elektronische Daten] [Arturo J. Fernández] 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. Springer-Verlag Berlin Heidelberg, 2000 Key words: Predictive likelihood nationallicence Type II double censoring nationallicence two-parameter exponential distribution nationallicence order statistics nationallicence https://doi.org/10.1007/s001840050046 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001840050046 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fernández Arturo J. 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 aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer