On the Alpha Power Transformed Power Inverse Lindley Distribution

Abstract

In this paper, we introduce a new generalization of the power inverse Lindley distribution referred to as the alpha power transformed power inverse Lindley (APTPIL). The APTPIL model provides a better fit than the power inverse Lindley distribution. It includes the alpha power transformed inverse Lindley, power inverse Lindley and inverse Lindley as special sub models. Various properties of the APTPIL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Important data set is employed to show how the proposed model works in practice.