A New Generalized Gamma Type II Exponentiated Half Logistic-Topp-Leone-G Family of Distributions with Applications

In this research, we introduce a novel family of distributions titled the Gamma Type II Exponentiated Half Logistic-Topp-Leone-G (RB-TIIEHLTL-G) distribution. The series expansion, order statistics, uncertainty measure, stochastic orders and moments are some of the mathematical and statistical properties that were derived. We estimated the parameters using various techniques including least squares, maximum likelihood, Anderson-Darling, and Cram´er-von-Mises. Based on the Monte Carlo simulation results, the maximum likelihood estimation method demonstrated superior performance compared to other estimation techniques examined, leading to its selection for estimating the model parameters. By fitting the RB-TII-EHL-TL-W distribution a special case of the RB-TII-EHL-TL-G family of distributions to two real-world data sets from different fields, we demonstrate its superiority over existing equi-parameter non-nested models in the literature.