The New Topp-Leone-Marshall-Olkin-Gompertz-G Family of Distributions: Properties, Different Estimation Techniques and Applications on Censored and Complete Data

A new family of distributions (FoD) called the Topp-Leone-Marshall-Olkin Gompertz-G is presented in this paper. Derivations of some statistical properties were carried out. The model parameters were estimated using five methods, including weighted least squares, maximum likelihood estimation, least squares, Cram\'er-von Mises, and Anderson Darling. The simulation experiment assessed the precision of the model parameters through the utilization of five estimation methods. To evaluate the adaptability and utility of this new FoD, three real-life datasets were analyzed using a special case from the developed family of distributions, one of which contained censored data. Remarkably, the new model showed exceptional performance when compared against six other non-nested models. This comparison highlighted its superiority and effectiveness in modeling real-life datasets.