Estimation of P(X > Y) for the power Lindley distribution based on progressively type II right censored samples. Issue 2 (22nd January 2020)

• Record Type: Journal Article
• Authors: Joukar, A.; Ramezani, M.; MirMostafaee, S. M. T. K.
• Is Part Of: Journal of statistical computation and simulation. Volume 90:Issue 2(2020)
• Page Start: 355
• Page End: 389
• Publication Date: 2020-01-22
• Subjects: Bayesian estimation -- loss function -- Metropolis-Hastings within Gibbs algorithm -- progressive censoring; 62F10 -- 62F15 -- 65C60; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1685994
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: In this study, we discuss the problem of estimating ρ = P ( X > Y ), when X and Y are two independent power Lindley random variables, based on progressively type II right censored order statistics. The maximum likelihood estimator of ρ and its asymptotic distribution, asymptotic interval estimator of ρ, Bayesian point estimators for ρ under symmetric and asymmetric loss functions as well as credible intervals for ρ are achieved when X and Y have a common parameter. Since it seems that the integrals pertaining to the Bayes estimation cannot be obtained in explicit forms, we propose the Metropolis-Hastings within Gibbs algorithm to find the approximate Bayes estimates of ρ . A simulation study is given in order to evaluate the proposed estimators and compare the different methods, developed in the paper. The corresponding results for the general case (when X and Y have no common parameters), as well as two examples, are also provided. The paper finishes with some remarks.