Generalization of Power Lindley Distribution: Properties and Applications

Abstract

This article introduces the generalized Kumaraswamy power Lindley (GKPL) distribution, a novel probabilistic model derived by combining the generalized Kumaraswamy (GK-G) family with the power Lindley (PL) distribution. The GKPL distribution encompasses a wide range of distributions, including Kumaraswamy power Lindley, Kumaraswamy Lindley, generalized power Lindley, generalized Lindley, power Lindley, and the well-known Lindley, as special cases. Fundamental properties are derived, such as the hazard rate function, survival function, quantile function, reverse hazard function, moments, mean residual life function, entropy, and order statistics. To determine the parameters of the GKPL distribution, four estimation methods, including maximum likelihood, least squares, Cramer-von Mises, and Anderson-Darling methods, are used to estimate the parameters of the GKPL distribution. The effectiveness of the estimation techniques is assessed by employing Monte Carlo simulations. The adaptability and validity of the proposed GKPL distribution are compared with alternative models, including the Kumaraswamy power Lindley (KPL), Extended Kumaraswamy power Lindley (EKPL), type II generalized Topp Leone-power Lindley (TIIGTLPL), exponentiated generalized power Lindley (EGPL), generalized Kumaraswamy Weibull (GKW), generalized Kumaraswamy log-logistic (GKLLo), and generalized Kumaraswamy generalized power Gompertz (GKGPGo) distributions, through analyses of three real datasets.