Comparison of the Bayesian and other Methods of Estimation of the Reliability Function for Exponentiated Inverted Weibull Distribution

Abstract

The aim of this paper is to develop and compare different type of estimators of reliability function R(t) for the Exponentiated Inverted Weibull (EIW) distribution. Through this study, the authors want to draw the attention of researchers to explore Bayesian methods of estimation using different priors, which outperforms other estimators of the reliability function. We proposed the estimators of the parameter of the distribution and reliability function for the EIW distribution using the classical methods such as maximum likelihood method, uniformly minimum variance unbiased estimation method, median method and by Bayesian methods using different priors such as Jeffery prior, modified Jeffery prior and extended Jeffery prior. The performances of the proposed estimators are compared through Monte Carlo simulation study and real data analysis is performed for a data set. To the best of author`s knowledge, the classical method using median method and; the Bayesian methods using Jeffery prior, modified Jeffery prior and extended Jeffery prior have not given much attention for the estimation of reliability function. The estimators proposed are explicit and perform better than the extensively investigated estimation methods such as maximum likelihood and uniformly minimum variance unbiased estimators. Here, we have proposed six estimators using different approaches to derive estimators of the parameter and reliability function, which are interesting and can be applied by other statistician to other models.