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In this article, we proposed an inverse Lindley distribution and studied itsfundamental properties such as quantiles, mode, stochastic ordering and entropymeasure. The proposed distribution is observed to be a heavy-taileddistribution and has a upside-down bathtub shape for its failure rate. Further,we proposed its applicability as a stress-strength reliability model forsurvival data analysis. The estimation of stress-strength parameters and$R=P[X>Y]$, the stress-strength reliability has been approached by bothclassical and Bayesian paradigms. Under Bayesian set-up, non-informative(Jeffrey) and informative (gamma) priors are considered under a symmetric(squared error) and a asymmetric (entropy) loss functions, and aLindley-approximation technique is used for Bayesian computation. The proposedestimators are compared in terms of their mean squared errors through asimulation study. Two real data sets representing survival of Head and Neckcancer patients are fitted using the inverse Lindley distribution and used toestimate the stress-strength parameters and reliability.

The inverse Lindley distribution: A stress-strength reliability model