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Journal of Probability and Statistics
Volume 2011, Article ID 457472, 17 pages
http://dx.doi.org/10.1155/2011/457472
Research Article

Bayesian Inference on the Shape Parameter and Future Observation of Exponentiated Family of Distributions

1Department of Statistics, St. Anthony's College, Shillong 793 001, India
2Department of Statistics, Visva-Bharati University, Santiniketan 731 235, India

Received 17 May 2011; Accepted 5 September 2011

Academic Editor: Mohammad Fraiwan Al-Saleh

Copyright © 2011 Sanku Dey and Sudhansu S. Maiti. 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.

Abstract

The Bayes estimators of the shape parameter of exponentiated family of distributions have been derived by considering extension of Jeffreys' noninformative as well as conjugate priors under different scale-invariant loss functions, namely, weighted quadratic loss function, squared-log error loss function and general entropy loss function. The risk functions of these estimators have been studied. We have also considered the highest posterior density (HPD) intervals for the parameter and the equal-tail and HPD prediction intervals for future observation. Finally, we analyze one data set for illustration.