Abstract
In this article, a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions. We call the new distribution, the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility for modeling lifetime data. The new distribution includes the inverse Lindley and the Marshall-Olkin inverse Lindley as special distributions. Essential properties of the generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated including, quantile function, ordinary moments, incomplete moments, moments of residual and stochastic ordering. Maximum likelihood method of estimation is considered under complete, Type-I censoring and Type-II censoring. Maximum likelihood estimators as well as approximate confidence intervals of the population parameters are discussed. A comprehensive simulation study is done to assess the performance of estimates based on their biases and mean square errors. The notability of the generalized Marshall-Olkin inverse Lindley model is clarified by means of two real data sets. The results showed the fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits than power Lindley, extended Lindley, alpha power transmuted Lindley, alpha power extended exponential and Lindley distributions.