CHOICE OF SUITABLE INFORMATIVE PRIOR FOR THE SCALE PARAMETER OF THE MIXTURE OF LAPLACE DISTRIBUTION

The major problem in Bayesian analysis is the choice of prior for the specified model. In the current study, the motivation is the comparsion of the informative priors for the mixture of Laplace distribution under different loss functions. A prior is selected based on the minimum posterior risks criteria where Bayes estimates and posterior risk are evaluated using the square error loss function, the precautionary loss function, the weighted squared error loss function and the modified (quadratic) squared error loss function. Bayes estimates and respective posterior risks are evaluated in terms of sample size, censoring rate and proportion of the component of the mixture using Levy and Gumbel Type-II informative priors. Limiting expressions for the complete sample are also derived. A real-life mixture data application has been discussed. The Elicitation of hyperparameters of mixture through prior predictive approach has also argued.