  In this article, we proposed an inverse Lindley distribution and studied its
fundamental properties such as quantiles, mode, stochastic ordering and entropy
measure. The proposed distribution is observed to be a heavy-tailed
distribution and has a upside-down bathtub shape for its failure rate. Further,
we proposed its applicability as a stress-strength reliability model for
survival data analysis. The estimation of stress-strength parameters and
$R=P[X>Y]$, the stress-strength reliability has been approached by both
classical 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 a
Lindley-approximation technique is used for Bayesian computation. The proposed
estimators are compared in terms of their mean squared errors through a
simulation study. Two real data sets representing survival of Head and Neck
cancer patients are fitted using the inverse Lindley distribution and used to
estimate the stress-strength parameters and reliability.
