A New Alternative to the Log-Kumaraswamy Distribution: Properties, Estimation, and Fitting Data

Statistical distributions play a crucial role in modelling real-life data in various fields. Recently, various statistical distributions have been proposed and used in real-life data analysis. This paper introduces a novel statistical distribution as an alternative to the log-Kumaraswamy distribution. It is called the power log-Kumaraswamy distribution. We explore several distributional properties of the suggested distribution. We consider nine estimation techniques, namely, maximum likelihood, Cramér-von Mises, maximum product of spacing, least squares, weighted least squares, Anderson–Darling, right-tailed Anderson–Darling, minimum spacing absolute distance, and minimum spacing absolute-log distance methods to estimate the parameters of the introduced distribution. The performances of these estimators are evaluated via an extensive Monte Carlo simulation study. Furthermore, the applicability and superiority of the power log-Kumaraswamy distribution are demonstrated through two practical data examples from engineering and health economics. The goodness-of-fit analysis’s results support the proposed distribution’s superiority over its main competitors.