The Marshall-Olkin Extended Gamma Lindley distribution: Properties, characterization and inference

Abstract In this research paper, we introduce a new three-parameter model called Marshall-Olkin Extended Gamma Lindley, which provides greater flexibility for modeling lifetime data. We investigate some of its structural properties, including moments and moment generating function. Furthermore, we prove that this model is identifiable. We corroborate that the Marshall-Olkin Extended Gamma Lindley distribution is characterized by its truncated moments of order statistics. Relying on this characterization and the least squares, we set forward a new method in order to estimate the unknown parameters of the proposed model. A comparative study is conducted between this approach and different classical methods of estimation. A real data set is applied to show the flexibility of the suggested model against other models.