The New Gamma Topp-Leone-Heavy Tailed-G Family of Distributions: Properties and Applications

This paper introduces a new and flexible family of distributions, namely the Gamma Topp-Leone-Heavy-Tailed-G distribution. Several statistical properties of the proposed family are derived, including the hazard rate function, quantile function, moments, moment generating function, Rényi entropy, distribution of order statistics and stochastic orderings. Parameter estimation is performed using various estimation techniques, including Maximum Likelihood (ML), Cramér-von Mises (CVM), Weighted Least Squares (WLS), and Least Squares (LS). In addition, the consistency and efficiency of the estimators are evaluated through a Monte Carlo simulation study. To demonstrate the flexibility and practical applicability of the proposed family, three real-world data sets from different application domains are analyzed.