Bayesian estimation of the mixture of exponentiated inverted Weibull distribution using noninformative and informative priors

In this study, Bayesian analysis of exponentiated inverted Weibull distribution (EIWD) is discussed. In particular, estimation of the scale parameter of the EIWD is focused whereas the shape parameter is assumed fixed. To derive the posterior distribution, uniform, Jeffreys, gamma and inverse Levy priors are used. Furthermore, to obtain Bayes estimates, the square error loss function (SELF), quadratic loss function (QLF), weighted loss function (WLF), precautionary loss function (PLF) and weighted balance loss function (WBLF) are considered. For comparison of the performance of different loss functions, the posterior risk is also calculated in this article. From application to the failure times of windshields dataset, results suggest that the uniform prior is a better prior than the Jeffreys prior, and WBLF is a suitable loss function for the estimation of the scale parameter of the mixture of EIWD. By comparing noninformative and informative priors, it is observed that the gamma prior has the minimum posterior risk.