Bayesian estimation for the type-I hybrid xgamma distribution using asymmetric loss function

Abstract

This article proposes the Bayes estimation of the parameter and reliability function for xgamma distribution in the presence of type-I hybrid censored observations. The Bayes estimate of the parameter has been obtained by assuming informative and non-informative priors using general entropy loss function. Obviously, censoring adds difficulties in estimation procedure; hence the Bayes estimators computed with type-I hybrid censored observation under the mentioned prior often do not assume any standard form. Therefore, Bayes estimates are computed using Tierney-Kadane approximation and Markov Chain Monte Carlo numerical technique. Further, different interval estimates namely asymptotic confidence interval, bootstrap confidence interval and highest posterior density interval along with the width of the interval and coverage probability are also discussed. The maximum likelihood estimate for the same has also been computed using non- linear maximization iterative procedure and compared with corresponding Bayes estimates using Monte Carlo simulations. The comparison of the estimators are made in terms of average loss over whole sample space and corresponding length of the interval. lastly, one medical data set has been considered for the real application of the proposed study.