Bayesian Estimation of Parameters under the Constant Shape Bi-Weibull Distribution Using Extension of Jeffreys? Prior Information with Three Loss Functions

The Weibull distribution has been observed as one of the most useful distributions, for modeling and analyzing lifetime data in Engineering, Biology, Survival and other fields. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. 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 Square Error Loss for estimating the Constant Shape Bi-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 (LINEX) Loss function in most cases gives the smallest Mean Square Error and Absolute Bias for both the scale parameter and the shape parameter for the given values of Extension of Jeffreys Prior. An illustrative example is also provided to explain the concepts.