In this paper, we introduce a new extension of the power Lindley distribution, called the odd log-logistic Marshall-Olkin power Lindley distribution. We discuss some of its properties such as the shapes of the density, hazard rate functions, quantile function, mixture representation, moments, and order statistics. We also obtain the estimators of the parameters through maximum likelihood approach. A simulation study is performed to evaluate the performance of the maximum likelihood estimators. Finally, two real data sets are applied to illustrating of the usefulness of the new model and to comparing the fit of the new distribution with those attained by some other extensions of the Lindley and power Lindley distributions.
