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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 589640, 13 pages
http://dx.doi.org/10.1155/2012/589640
Research Article

Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions

1Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Salangor, Malaysia
2Department of Mathematics, University Putra Malaysia, 43400 Serdang, Salangor, Malaysia

Received 18 April 2012; Revised 29 May 2012; Accepted 12 June 2012

Academic Editor: Bohdan Maslowski

Copyright © 2012 Chris Bambey Guure et al. 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 Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameter α and the shape parameter β for the given values of extension of Jeffreys' prior.