Exact expressions for single and product moments of generalized order statistics are derived when the underlying population is assumed to have a Rayleigh distribution. Bayesian estimators and highest posterior density (HPD) credible intervals are obtained for the scale parameter and reliability function based on generalized order statistics. We also derive the Bayes predictive estimator and HPD...

In this paper, the statistical inference of the unknown parameters of a twoparameter inverse Weibull (IW) distribution based on the progressive Type-II censored sample has been considered. The maximum likelihood estimators cannot be obtained in explicit forms, hence the approximate maximum likelihood estimators are proposed, which are in explicit forms. The Bayes and generalized Bayes estimator...

X1, . . . , Xn iid ∼ N (θ, σ), with σ known. Our goal is to estimate θ under squared-error loss. For our first guess, pick the natural estimator X. Note that it has constant risk σ 2 n , which suggests minimaxity because we know that Bayes estimators with constant risk are also minimax estimators. However, X is not Bayes for any prior, because under squared-error loss unbiased estimators are Ba...

The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A re...

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey’s scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we ha...

The study aims to estimate the parameter of the Generalized Pareto Distribution under Type II censored samples. The Bayes Estimators have been derived under a class of informative and non-informative Priors using different symmetric and asymmetric Loss functions. The Credible Intervals, Highest Posterior Density (HPD) intervals, Posterior Predictive Distributions and Posterior Predictive Interv...

This paper considers inference under progressive type II censoring with a compound Rayleigh failure time distribution. The maximum likelihood (ML), and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters, namely reliability and hazard functions. We obtained Bayes estimators using the conjugate priors for two shape and scale parameters. When the two p...

This paper deals with the problem of selecting good negative binomial populations as compared with a standard or a control. The main results are based on the use of the empirical Bayes approach. First we derive the monotone empirical Bayes estimators of the concerned parameters. Based on these estimators, we construct monotone empirical Bayes selection rules. Asymptotic optimality properties of...

• In this paper, we propose Bayes estimators of the parameter of the exponentiated gamma distribution and associated reliability function under General Entropy loss function for a censored sample. The proposed estimators have been compared with the corresponding Bayes estimators obtained under squared error loss function and maximum likelihood estimators through their simulated risks (average l...