The new transmuted-H family of distributions: theory, simulation, and real-world applications

This study introduces a new transmuted-H (NT-H) family of probability distributions for modeling data on the bounded unit interval. The proposed family is generated through a flexible transmutation-based mechanism that enhances the shape adaptability of existing baseline models. Statistical inference for the proposed family is carried out using the maximum likelihood estimation (MLE) method. Several mathematical properties of the NT-H family are derived, with special emphasis on the new Transmuted Kumaraswamy (NTKw) distribution. Its structural and inferential properties are analytically investigated, and the performance of the MLEs is assessed through a Monte Carlo simulation study. To demonstrate practical applicability, the NTKw distribution is applied to two real datasets on bounded unit intervals. Its goodness-of-fit performance is compared with the classical Kumaraswamy and transmuted Kumaraswamy models. The results indicate that the NTKw model provides a comparatively better fit among the considered models, highlighting its flexibility and usefulness for modeling bounded data.