Alpha Power Transformed Extended power Lindley Distribution

The Lindley distribution has been generalized by several researchers in recent years. In this paper, we introduce and study a new generalization of extended power Lindley distribution named alpha power transformed extended power Lindley ( APTEPL ) distribution that provides better fits than the extended Power Lindley distribution and existing generalizations. It includes the alpha power transformed power Lindley, alpha power transformed extended Lindley, alpha power transformed Lindley, extended power Lindley, power Lindley, extended Lindley and Lindley distribution as a special cases. In this article various properties of the APTEPL distribution such as moments, moment generating function, Characteristic function and cumulant generating function, quantiles and Order Statistics are derived. Method of maximum likelihood estimation is used to obtain the model parameters. A simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters. Two data sets have been utilized to show how the APTEPL distribution works in practice.