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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)
##### Software:
ADGofTest; CODA; Gibbsit; lamW; nleqslv; R; truncnorm
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