On Bayesian Analysis of Burr Type VII Distribution under Different Censoring Schemes

This paper includes the Bayesian analysis of Burr type VII distribution. Three censoring schemes, namely, left censoring, singly type II censoring, and doubly type II censoring have been used for posterior estimation. The results of different censoring schemes have been compared with those under complete samples. The comparative study among the performance of different censoring schemes has also been made. Two noninformative (uniform and Jeffreys) priors have been assumed to derive the posterior distributions under each case. The performance of Bayes estimators has been compared in terms of posterior risks under a simulation study. 1. Introduction Burr [1] introduced twelve forms of the Burr distribution. However, most of the authors have considered the estimation of Burr type XII distribution. The Burr type VII distribution has rarely received any attention. Wahed [2] presented Bayes estimators for the parameters of Burr type XII distribution under the symmetric squared error loss function and the asymmetric linear exponential loss function based on a simple prior distribution. As the estimator turns out to be ratios of integrals, different approximation techniques have been used to obtain approximate Bayes estimators. Real life example has been used to demonstrate the application of Burr type XII distribution. Dasgupta [3] discussed that under certain conditions, the distribution of Burr can be shown to follow an extreme value distribution. Hence, a result on extremal process based on stationary sequence has been proved. Some data sets have been analyzed, and applications of the results have been indicated. Makhdoom and Jafari [4] obtained Bayesian estimators for the shape parameter of the Burr Type XII distribution using grouped and ungrouped data and also consider relationship between them. Bayes point and interval estimators have been derived. Squared error and precautionary loss functions have been considered for the posterior analysis. Monte Carlo simulation has been used to compare the performance of different estimators. Panahi and Asadi [5] considered the statistical inferences based on a Type-II hybrid censored sample from a Burr type XII distribution. As the maximum likelihood estimators cannot be obtained in closed form, a simple fixed point type algorithm has been proposed to compute the maximum likelihood estimators. The approximate confidence intervals for the parameters based on the s-normal approximation to the asymptotic distribution of MLE have been constructed. Bayes estimates of the unknown parameters have also been obtained under