IMPROVED INFORMATIVE PRIOR FOR THE MIXTURE OF LAPLACE DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS
Keywords:
Censored Sampling; Inverse Transformation Method; Squared Error Loss Function (SELF); Precautionary Loss Function; Hyperparameters; Prior Elicitation; Fixed Test Termination Time; Mixture Distribution; Posterior Risk; Improved Informative Prior.Abstract
In this study, a new informative prior is developed for the scale parameter of the mixture of Laplace distribution when data is censored and can be used to model various real world problems. The basic proposal is to merge both informative and non-informative priors for improvement of prior information. There are many real world problems in which investigator has different opinion than prior information e.g. one doctor provides information that the harmfulness of medicine is 20% and another chemist observes the chemical combination of medicine and thinks that medicine is harmful 30% due to one element, so if we combine both doctor and chemist opinion as a prior our analysis will improve. An inclusive simulation scheme including a large number of parameter is followed to highlight properties and behavior of the estimates in terms of sample size, censoring rate and proportion of the component of the mixture. A simulated mixture data with censored observations is generated by probabilistic mixing for computational purposes. Elegant closed form expressions for the Bayes estimators and their posterior risk are derived for the censored sample as well as for the complete sample. Some interesting comparison and properties of the estimates are observed and presented. The complete sample expressions for ML estimates and for their variances are derived and also the components of the information matrix are constructed as well. The Elicitation of hyper-parameters of mixture through prior predictive approach and a real-life mixture data example has also been discussed. The Bayes estimates are evaluated under squared error loss function and precautionary loss function.
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