A New Cosine Topp–Leone Exponentiated Half Logistic-G Family of Distributions with Applications

A new generalized family of distributions, termed the Cosine–Topp–Leone–Exponentiated Half Logistic–G (Cos–TL–EHL–G) family, is proposed. The primary motivation for introducing this family is to enhance the modelling flexibility of the existing Cosine–Topp–Leone–G class by incorporating a exponentiated half logistic (EHL-G)-based transformation. Two important special cases, namely the Cos–TL–EHL–Weibull (Cos–TL–EHL–W) and Cos–TL–EHL–Log–Logistic (Cos–TL–EHL–LLoG) distributions, are presented. Several mathematical and statistical properties of the proposed family are derived, including series expansions, moments, order statistics, and uncertainty measures. Parameter estimation is carried out using maximum likelihood, least squares, Anderson–Darling, and Cramér–von Mises methods. A Monte Carlo simulation study indicates that the maximum likelihood estimator outperforms the competing estimation techniques. The practical usefulness and robustness of the proposed family are illustrated through applications to two real datasets, where the Cos–TL–EHL–W distribution demonstrates superior performance compared to both nested and non-nested competing models.