The inverse Lindley distribution: A stress-strength reliability model

In this article, we proposed one parameter, inverse Lindley distribution, with its fundamental properties such as quantiles, mode, stochastic ordering, entropy, and stress–strength reliability. The proposed distribution has upside-down bathtub shape for its failure rate function. The estimation of stress–strength reliability has been approached by both classical and Bayesian methods. Under Bayesian set-up, both non-informative (Jeffrey) and informative (gamma) priors are considered under symmetric (squared error) and asymmetric (entropy) loss functions. The Lindley’s approximation method is used for Bayesian computation. The performances of the estimators have been compared in terms of their mean squared errors using simulated samples. Two real data-sets, representing the survival times of head and neck cancer patients, are considered for demonstrating the applicability of the proposed model.