Unit Power Lindley Distribution: Properties and Estimation

This paper introduces the unit power Lindley distribution and presents its fundamental statistical properties, such as density and cumulative distribution functions, hazard rate functions, and, their characteristics, moments, and related measures. The parameters of this newly proposed distribution are estimated by using six different methods: maximum likelihood, least squares, weighted least squares, Cramér von Mises, Anderson Darling, and right-tail Anderson Darling. The performances of the considered estimation methods are compared through an extensive Monte Carlo simulation study. Additionally, two real datasets are modeled to demonstrate that the unit power Lindley distribution provides a significantly better fit than compared to commonly used unit distributions.