The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

Abstract

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data. We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Rényi entropy, Shannon entropy, and order statistics of the proposed distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters. Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained. Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk. The flexibility and importance of the proposed distribution are illustrated by means of four real datasets.