Estimation of P(X > Y) for the power Lindley distribution based on progressively type II right censored samples

ABSTRACT

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 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.

Keywords:

• Bayesian estimation
• loss function
• Metropolis-Hastings within Gibbs algorithm
• progressive censoring

2010 Mathematics Subject Classifications:

• 62F10
• 62F15
• 65C60

Acknowledgments

We would like to thank the referee for his/her valuable comments which improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.