Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application

Accepted - December 2022

Abstract

The purpose of the present paper is two-fold. First, we consider the estimation of the unknown model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution when a progressively type-II censored sample (PT-IICS) is available. The sufficient condition for the existence and uniqueness of the maximum likelihood estimates (MLE) is obtained. We compute MLEs using the expectation-maximization (EM) algorithm. Asymptotic confidence intervals are constructed. For comparison purposes, confidence intervals using bootstrap-p and bootstrap-t methods are also constructed. Bayes estimates are derived with respect to the squared error, LINEX, and the entropy loss functions. Two approximation techniques (Lindley and importance sampling) are used for the computation of the Bayes estimates. Further, the highest posterior density (HPD) credible intervals are derived using the importance sampling method. Second, we consider the problem of Bayesian prediction. Prediction estimates and the associated prediction equal-tail intervals under one-sample and two-sample frameworks are obtained. A simulation study is conducted the comparison the methods of estimation and prediction. Finally, a real dataset is considered and analyzed for the purpose of illustration.