IMPROVED INFORMATIVE PRIOR FOR THE MIXTURE OF LAPLACE DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

In this study, a new informative prior is developed for the scale parameter of themixture of Laplace distribution when data is censored and can be used to model various realworld problems. The basic proposal is to merge both informative and non-informative priors forimprovement of prior information. There are many real world problems in which investigator hasdifferent opinion than prior information e.g. one doctor provides information that the harmfulnessof medicine is 20% and another chemist observes the chemical combination of medicine andthinks that medicine is harmful 30% due to one element, so if we combine both doctor andchemist opinion as a prior our analysis will improve. An inclusive simulation scheme including alarge number of parameter is followed to highlight properties and behavior of the estimates interms of sample size, censoring rate and proportion of the component of the mixture. A simulatedmixture data with censored observations is generated by probabilistic mixing for computationalpurposes. Elegant closed form expressions for the Bayes estimators and their posterior risk arederived for the censored sample as well as for the complete sample. Some interesting comparisonand properties of the estimates are observed and presented. The complete sample expressions forML estimates and for their variances are derived and also the components of the informationmatrix are constructed as well. The Elicitation of hyper-parameters of mixture through priorpredictive approach and a real-life mixture data example has also been discussed. The Bayesestimates are evaluated under squared error loss function and precautionary loss function.