Scale Parameter Estimation of the Laplace Model Using Different Asymmetric Loss Functions

Abstract

In the last few decades, there has been an emergent interest in the construction of flexible parametric classes of probability distributions in Bayesian as compared to Classical approach. In present study Bayesian Analysis of Laplace model using Inverted Gamma, Inverted Chi-Squared informative, Levy and Gumbel Type-II priors is discussed. The properties of posterior distribution, credible interval, highest posterior density region (HPDR) and Bayes Factor are discussed in current study. Bayes estimators are derived under squared error loss function (SELF), precautionary loss function, weighted squared error loss function and modified (quadratic) squared error loss function. Hyperparameters are determined through Empirical Bayes method. The estimates are also compared using the posterior risks (PRs) under the said loss functions. The priors and loss functions are compared using a real life data set.