Extending the Kumaraswamy distribution: properties and applications - Jan, Mahvish; Ahad, Tabasum; Correa, Fabio Mathias; Ahmad, S. P. (Frontiers in Applied Mathematics and Statistics, 2026)
In this study, we propose a new extension of the Kumaraswamy distribution, termed the PNJKumaraswamy Distribution, developed using the PNJ transformation technique. The PNJKumaraswamy distribution provides enhanced flexibility compared to several existing generalizations of the Kumaraswamy model. We derive and examine its key statistical properties, including moments, quantiles, hazard rate behavior and related structural measures. The parameter estimation is performed using the maximum likelihood method. A simulation study is conducted to evaluate the behavior of the maximum likelihood estimates under various parameter settings. The practical usefulness of the proposed model is further demonstrated through the analysis of real data sets, where the PNJKumaraswamy distribution achieves a superior fit relative to competing models.