Bayesian and E-Bayesian Estimation for The Inverted Topp-Leone Distribution Based on Progressive Type-I Censoring Data

Abstract

In this paper, Bayesian, E-Bayesian, and non-Bayesian estimations of the shape parameter of the inverted Topp-Leone
distribution are studied based on the progressive Type I censored (PT-IC) data. The maximum likelihood estimator (MLE), Bayes, and
E-Bayes estimators of the unknown parameter under the squared error loss (SEL) function, degroot loss (DL) function, and quadratic
loss (QL) function are obtained. For E-Bayes estimates, we assumed three distributions for the hyper-parameters a and b. Three types
of confidence intervals are discussed for the unknown parameter. The effectiveness of the suggested approaches is compared using a
simulated study, and for illustration, two numerical cases have been examined.