On A New Extended Log-Normal Distribution: Properties, Regression, Bayesian Regression, and Data Analysis

This article introduces and investigates the Marshall-Olkin Topp-Leone log-normal (MOTLLN) distribution, a novel extension of the log-normal distribution. It can be presented as a new four-parameter continuous distribution designed to analyze a wide range of versatile positive-valued data. In a brief first part, we explore its main aspects, including the quantile function and the hazard rate function. We then focus on its applied aspect from a statistical perspective. Parameter estimation is performed using both maximum likelihood and Bayesian methods. Furthermore, we employ the MOTLLN distribution to develop a parametric regression model and a Bayesian regression model, demonstrating its versatility. A simulation study supports the practical performance of the maximum likelihood estimation procedure. Real datasets are used to demonstrate the applicability of our methodology. The effectiveness of the additional parameter in the MOTLLN model is assessed by a likelihood ratio test. In addition, the parametric bootstrap method is used to evaluate the suitability of the MOTLLN model for the datasets. All the results obtained confirm the great potential of the proposed model in all aspects.