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Estimation of \(P(X > Y)\) for the power Lindley distribution based on progressively type II right censored samples. (English) Zbl 07194290
Summary: In this study, we discuss the problem of estimating \(\rho =P(X>Y)\), 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 \(\rho\) and its asymptotic distribution, asymptotic interval estimator of \(\rho\), Bayesian point estimators for \(\rho\) under symmetric and asymmetric loss functions as well as credible intervals for \(\rho\) 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 \(\rho\). 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.
Reviewer: Reviewer (Berlin)
MSC:
62F10 Point estimation
62F15 Bayesian inference
65C60 Computational problems in statistics (MSC2010)
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