On the Topp-Leone log-normal distribution: Properties, modeling, and applications in astronomical and cancer data

In the realm of astronomy, the two-parameter log-normal distribution has ominous implications. In this article, we propose a new version of the two-parameter log-normal distribution with an application to astronomical data. More precisely, a new modulating parameter is added to the two-parameter log-normal distribution through the use of the Topp-Leone generator of distributions. The moments, quantile function, several reliability measures, and other significant aspects of the proposed distribution are investigated. The maximum likelihood approach and a Bayesian technique are both utilized to estimate the unknown parameters. In addition, we present a parametric regression model and a Bayesian regression method. A simulation study is carried out to assess the long-term performance of the estimators of the distribution parameters. Two real datasets are employed to show the applicability of this new distribution. The efficiency of the newly added parameter is tested by utilizing the likelihood ratio test. The parametric bootstrap approach is also utilized to determine the adequacy of the suggested model for the datasets.