On the Bayesian analysis of 3-component mixture of exponential distributions under different loss functions

Abstract

The memory-less property of the Exponential distribution is a strong reason of its use for testing lifetimes of objects in many lifetime modeling applications. Also, mixture models have extensively been used in survival analysis and reliability studies. This article focuses on the Bayesian analysis of the 3-component mixture of Exponential distributions under type-I right censoring scheme. Taking different noninformative and informative priors, Bayes estimators and posterior risks for the unknown parameters (parameters of component distributions and mixing proportions) are derived under squared error loss function, precautionary loss function and DeGroot loss function. The elicitation of the hyperparameters is also done using prior predictive distribution.The Bayes estimators and posterior risks are looked at as a function of the test termination time. Some important properties and comparisons of the Bayes estimates are presented. Simulated results and real data example are also given to illustrate the study.

Keywords

• 3-Component mixture distribution,Non-informative and informative priors,Loss function,Bayes estimators,Posterior risks,Test termination time

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