Bayesian Estimation of Transmuted Lomax Mixture Model with an Application to Type-I Censored Windshield Data

Abstract

Transmuted distributions have been centered of focus for researchers recently due to their flexibility and applicability in statistics. However, the only few contributions have considered estimation for mixture of transmuted lifetime models especially under Bayesian methods has been explored more recently. We have considered the Bayesian estimation of transmuted Lomax mixture model (TLMM) for type-I censored samples. The Bayes estimates (BEs) for informative and non-informative priors. The BEs and posterior risks (PRs) are evaluated using four different loss functions (LFs), two symmetric and two asymmetric, namely the squared error loss function (SELF), precautionary loss function (PLF), weighted balance loss function (WBLF), and general entropy loss function (GELF). Simulations are run using Lindley Approximation method to compare the BEs under various sample sizes and censoring rates. The estimates under informative prior and GELF were found superior to their counterparts. The applicability of the proposed estimates has been illustrated using the analysis of a real data regarding type-I censored failure times of windshields airplanes.