Bayesian Estimation of Transmuted Weibull Distribution under Different Loss Functions

Abstract

In this article, we aim to estimate the parameters of the transmuted Weibull distribution (TWD) using Bayesian approach, as the Weibull distribution plays an important role in reliability engineering and life testing problems. Informative and non-informative priors under squared error loss function (SELF), precautionary loss function (PLF) and quadratic loss function (QLF) are assumed to estimate the scale, the shape and the transmuted parameter of the TWD. In addition to this, we also compute the Bayesian credible intervals (BCIs). To estimate parameters, we adopt Markov Chain Monte Carlo (MCMC) technique assuming uncensored and censored environments in terms of different sample sizes and censoring rates. The posterior risks, associated with each estimator are used to compare the performance of different estimators. Two real data sets are analyzed to illustrate the flexibility of the proposed distribution.

Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction

“…Moreover, numerous methods have been used to estimate the parameters and survival function in the Bayesian method. For example, Upadhyay and Gupta [17]; Monfared et al [18]; Yousaf et al [19]; Soliman et al [20]; and Al Omari [21] discussed some Bayesian estimations using the MH algorithm to estimate parameters in various censored data and priors.…”