A Type I Generalized Logistic Distribution: Solving Its Estimation Problems with a Bayesian Approach and Numerical Applications Based on Simulated and Engineering Data

The family of logistic type distributions has been widely studied and applied in the literature. However, certain estimation problems exist in some members of this family. Particularly, the three-parameter type I generalized logistic distribution presents these problems, where the parameter space must be restricted for the existence of their maximum likelihood estimators. In this paper, motivated by the complexities that arise in the inference under the likelihood approach utilizing this distribution, we propose a Bayesian approach to solve these problems. A simulation study is carried out to assess the performance of some posterior distributional characteristics, such as the mean, using Monte Carlo Markov chain methods. To illustrate the potentiality of the Bayesian estimation in the three-parameter type I generalized logistic distribution, we apply the proposed method to real-world data related to the copper metallurgical engineering area.