Classical and Bayesian Estimation for 2-Component Mixture of Generalized Rayleigh Distribution based on Type I Censored Samples

Abstract

Mixture models are more appealing and appropriate for studying the heterogeneous nature of lifetimesof certain mechanical, biological, social, economic and several other processes as compared tosimple models. This paper considers mixture of generalized Rayleigh distributions under classical andBayesian perspective based on type I censored samples. The new distribution which exhibits decreasing,decreasing-increasing-decreasing, unimodal and bimodal shaped density while the distribution has theability to model lifetime data with increasing, increasing-decreasing-increasing, bathtub and bi-bathtubshapedfailure 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. Infrequentist method, the maximum likelihood estimate of the parameters and their asymptotic condenceintervals are obtained while for Bayesian analysis, the squared error loss function (SELF) and uniformas well as beta and gamma priors are considered to obtain the Bayes estimators of the unknown parametersof the model. Furthermore, highest posterior density (HPD) credible intervals are also obtained.In real data analysis, in addition to point estimates of the model parameters, asymptotic condenceintervals and HPD credible intervals, two bootstrap CIs are also provided. Monte Carlo simulationstudy is performed to assess the behavior of these estimators. An application of the model is presentedby re-analyzing strength for single carbon bers data set.