Parameter (shape) Estimation of Weibull-Exponential Distribution Using Classical and Bayansian Approach Under Different Loss Functions

Abstract

The Bayesian as a statistical approach is a method applied in statistical inference which helps researchers to incorporate prior information surrounding the population parameter with support from information embodied in a sample to guide the inference process. From the Bayesian viewpoint, the choice of prior depends on the one’s wide knowledge of the subject matter, since there is no obvious approach from which one can decisively conclude that one prior  has edge over the other.  This paper aim at studied the parameter (shape) of Weibull-exponential distribution via classical and the Bayesian approach. Different estimates of the parameter (shape) were obtained from the Bayesian approach using quasi and extended Jeffery priors, under various loss functions. The results shows that the quadratic loss functions under extended Jeffrey prior and quasi prior outperformed the squared error loss function and the precautionary loss function across different sample sizes. The result also reveals that the Bayesian estimate of the parameter (shape) under extended Jeffrey and quasi prior using quadratic loss function is better than the maximum likelihood estimate. Finally, it was deduced that, an increment in  the sample size, makes the error to reduce and the estimates approach the real value of the parameter (shape).