Bayesian Inference of a Finite Mixture of Inverse Weibull Distributions with an Application to Doubly Censoring Data

Abstract

The families of mixture distributions have a wider range of applications in different fields such as fisheries, agriculture, botany, economics, medicine, psychology, electrophoresis, finance, communication theory, geology and zoology. They provide the necessary flexibility to model failure distributions of components with multiple failure modes. Mostly, the Bayesian procedure for the estimation of parameters of mixture model is described under the scheme of Type-I censoring. In particular, the Bayesian analysis for the mixture models under doubly censored samples has not been considered in the literature yet. The main objective of this paper is to develop the Bayes estimation of the inverse Weibull mixture distributions under doubly censoring. The posterior estimation has been conducted under the assumption of gamma and inverse levy using precautionary loss function and weighted squared error loss function. The comparisons among the different estimators have been made based on analysis of simulated and real life data sets.