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Journal of Probability and Statistics
Volume 2014, Article ID 809706, 7 pages
Research Article

Risk Efficiencies of Empirical Bayes and Generalized Maximum Likelihood Estimates for Rayleigh Model under Censored Data

1Department of Statistics, H. L. Institute of Commerce, Ahmedabad University, Ahmedabad 380009, India
2Department of Statistics, School of Sciences, Gujarat University, Ahmedabad 380009, India

Received 13 February 2014; Accepted 18 June 2014; Published 2 July 2014

Academic Editor: Shesh N. Rai

Copyright © 2014 Dinesh Barot and Manhar Patel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The comparison of empirical Bayes and generalized maximum likelihood estimates of reliability performances is made in terms of risk efficiencies when the data are progressively Type II censored from Rayleigh distribution. The empirical Bayes estimates are obtained using an asymmetric loss function. The risk functions of the estimates and risk efficiencies are obtained under this loss function. A real data set is presented to illustrate the proposed comparison method, and the performance of the estimates is examined and compared in terms of risk efficiencies by means of Monte Carlo simulations. The simulation results indicate that the proposed empirical Bayes estimates are more preferable than the generalized maximum likelihood estimates.