Bayesian Estimation of Transmuted Weibull Distribution under Different Loss Functions

  • Rahila Yousaf Department of Mathematics and Statistics, Riphah International University, Islamabad 46000, Pakistan
  • Sajid Ali Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
  • Muhammad Aslam Department of Mathematics and Statistics, Riphah International University, Islamabad 46000, Pakistan
Keywords: Transmuted Weibull distribution, loss functions, Bayes estimators, posterior risks, uniform prior, informative prior, BCIs, MCMC, censoring and chi-square test

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.

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Author Biographies

Rahila Yousaf, Department of Mathematics and Statistics, Riphah International University, Islamabad 46000, Pakistan

Rahila Yousaf recently completed her PhD in Statistics from Riphah International University, Islamabad. Her research interests are probability distributions and Bayesian inference

Sajid Ali, Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan

Sajid Ali is an assistant professor at the Department of Statistics, Quaid-i-Azam University (QAU), Islamabad, Pakistan. He did his PhD in Statistics from Bocconi University, Milan, Italy. His research interest is focused on Bayesian inference, construction of new flexible probability distributions, and process monitoring.

Muhammad Aslam, Department of Mathematics and Statistics, Riphah International University, Islamabad 46000, Pakistan

Muhammad Aslam is a professor at the Riphah International University, Islamabad. Prior to this position, he served as a Professor and Chairman department of Statistics at Quaid-i-Azam University, Islamabad, Pakistan. He supervised more than 200 MPhil and 20 PhD students. He has published more than 150 articles in well reputed international journals. He completed his PhD from University of Wales, UK. His research interests are Bayesian inference, Paired comparison modelling and mathematical statistics.

Published
2020-12-30
Section
Articles