The New Topp-Leone Exponentiated Half Logistic-Gompertz-G Family of Distributions with Applications

This research introduces a new family of distributions (FoD) titled the Topp-Leone Exponentiated-Half-Logistic-Gompertz-G (TL-EHL-Gom-G) distribution. The study explores a variety of statistical properties of the developed family, such as the quantile function, series expansion, order statistics, entropy, stochastic orders and moments. Through Monte Carlo simulations, various estimation techniques were compared, including the least squares (LS), Anderson Darling (AD), maximum likelihood (ML) and Cram\'er-von-Mises (CVM) methods via root mean square error (RMSE) and average bias (Abias). The results indicated that the ML estimation method performed better than other methods, hence, the selection for estimating the model parameters. To showcase the usefulness, robustness and applicability of the model, we applied it to three real-life data, including dataset with censored observations. The TL-EHL-Gom-W distribution, a special case of the TL-EHL-Gom-G FoD showed superiority over nested and non-nested models.