Statistical Analysis of the Lifetime Mixture Models under Bayesian Approach

Abstract

'l'lli::; llw::;i::; deal::; wiLh s l. i:l.t i::; t ical analysis of t he lifetillle ll1ixL llle models uuder B8ye::;iall approach. Type-I right censored s8 mpling scheme is used. Choice of distribution is made keeping ill view the originality and applicability. These contaiu Inverse Rayleigh, G Ullmbel Type- II , Frechet , Inverse Weibull and Inverted Exponential distribut ions. These lllixtlll'es di::;tribution have not been explored so far in Bayesian setup. Bayes estimators for t he parameters of the mixture models are derived in closed fOrtll using type-I right censoring. To conduct Bayesian analysis, informat ive and 11oniuformative priors are considered "vhile three different loss functions, Squared error loss function, Precaut ionary loss function and DeGroot loss function are employed . A thorough simulation study is made to scrutinize the properties of proposed Bayes estimators. For l he Inverse vVeibull model, when all the parameters are unknowll, Bayes estimators C8n not be gained in closed form, thus importance sampling t echnique is used to get t he Bayes estimate ill t his case. For the elicitation of hyperparametrs , we used prior predictive and prior mean method. Limiting expressions of the Bayes estimators and their corresponding posterior risks are also deri ved. For the Inverse \i\feibull distribution, Bayes estimators and the posterior risks for reliability function are also discussed . Grapllicalrepresentatioll of t he simulation analysis res ul ts are also presented for each ll1ixtme model. Applications of these mixture models are also offered by applying a real data set in each case.