Inferential analysis for the reliability parameter based on the three-parameter Lindley distribution

ABSTRACT

In this article, we consider the estimation of R = P(Y < X), when Y and X are two independent three-parameter Lindley (LI) random variables. On the basis of two independent samples, the modified maximum likelihood estimator along its asymptotic behavior and conditional likelihood-based estimator are used to estimate R. We also propose sample-based estimate of R and the associated credible interval based on importance sampling procedure. A real life data set involving the times to breakdown of an insulating fluid is presented and analyzed for illustrative purposes.