A new power transformed distribution with applications to radiotherapy and environmental datasets

Abstract

This study proposes the power type II Topp-Leone half logistic (P$T_{II}TLHL$) distribution, an extension of the type II Topp-Leone half logistic ($T_{II}TLHL$) distribution, achieved through the power transformation technique. The P$T_{II}TLHL$ distribution enhances the flexibility and applicability of the original model, making it suitable for a wider range of real-world datasets exhibiting complex features such as skewness, heavy tails, and high variability. Key features of the proposed distribution include a flexible unimodal and right-skewed probability density function, an explicit quantile function, and a versatile hazard rate function that accommodates both increasing and decreasing patterns. Several important properties of the P$T_{II}TLHL$ distribution are derived, including central moments, incomplete moments, conditional moments, probability-weighted moments, entropy measures, and order statistics. The parameters of the P$T_{II}TLHL$ distribution were estimated using 16 classical methods, supported by a simulation study to assess the performance of these estimators. Real-world applications to biomedical and environmental datasets demonstrate that the P$T_{II}TLHL$ distribution outperforms several existing models, establishing it as a powerful tool for modeling complex data in diverse fields.