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.

The study of system safety and reliability has always been vital for the quality and manufacturing engineers of varying fields for which generally the continuous probability distributions are proposed. Bivariate and multivariate continuous distributions are the candidates while studying more than one characteristic of the system. In this article, an attempt is made to address this issue when the reliability systems generate bivariate and correlated count datasets. The bivariate generalized geometric distribution (BGGD) is believed to serve as a potential candidate to model such types of datasets. Bayesian approach of data analysis has the potential of accommodating the uncertainty associated with the model parameters of interest using uninformative and informative priors. A real life bivariate correlated dataset is analyzed in Bayesian framework and the results are compared with those produced by the classical approach. Posterior summaries including posterior means, highest density regions, and predicted expected frequencies of the bivariate data are evaluated. Different information criteria are evaluated to compare the inferential methods under study. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) set-up of data augmentation implemented through WinBUGS.

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration.

The q-Weibull distribution is a generalized form of the Weibull distribution and has potential to model complex systems and life time datasets. Bayesian inference is the modern statistical technique that can accommodate uncertainty associated with the model parameters in the form of prior distributions. This study presents Bayesian analysis of the q-Weibull distribution using uninformative and informative priors and the results are compared with those produced by the classical maximum likelihood (ML) and least-squares (LS) estimation method. A simulation study is also made to compare the two methods. Different model selection criteria and predicted datasets are considered to compare the inferential methods under study. Posterior analyses include evaluating posterior means, medians, credible intervals of highest density regions, and posterior predictive distributions. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) setup using WinBUGS package. The Bayesian method has proved to be superior to its classical counterparts. A real dataset is used to illustrate the entire inferential procedure.