R = P(Y < X) for unit-Lindley distribution: inference with an application in public health

Abstract: The unit-Lindley distribution was recently introduced in the literature as a viable alternative to the Beta and the Kumaraswamy distributions with support in (0; 1). This distribution enjoys many virtuous properties over the named distributions. In this article, we address the issue of parameter estimation from a Bayesian perspective and study relative performance of different estimators through extensive simulation studies. Significant emphasis is given to the estimation of stress-strength reliability employing classical as well as Bayesian approach. A non-trivial useful application in the public health domain is presented proposing a simple metric of discrepancy.