Classical and Bayesian Estimations for a 2-Component Generalized Rayleigh Mixture Model under Type I Censoring

Mixture models are more appealing and appropriate for studying the heterogeneous nature of lifetimes of certain mechanical, biological, social, economic and several other processes as compared to simple models. This paper considers a mixture of generalized Rayleigh distributions under classical and Bayesian perspectives based on type I censored samples. The new distribution which exhibits decreasing, decreasing-increasing-decreasing, unimodal and bimodal shaped density while the distribution has the ability to model lifetime data with increasing, increasing-decreasing-increasing, bathtub and bi-bathtub-shaped failure rates. We derive some basic and structural properties of the proposed distribution. Moreover, we estimate the parameters of the model by using frequentist and Bayesian approaches. In frequentist method, the maximum likelihood estimate of the parameters and their asymptotic confidence intervals are obtained while for Bayesian analysis, the squared error loss (SEL) function and uniform as well as beta and gamma priors are considered to obtain the Bayes estimators of the unknown parameters of the model. Furthermore, the highest posterior density (HPD) credible intervals are also obtained. In real data analysis, in addition to point estimates of the model parameters, asymptotic confidence intervals and HPD credible intervals, two bootstrap CIs are also provided. Monte Carlo simulation study is performed to assess the behavior of these estimators. An application of the model is presented by re-analyzing strength for single carbon fibers data set.