A New Generalized Fisk distribution: Its Properties, Characterizations and Applications

The shortcomings of the traditional univariate distributions in the past greatly encouraged mathematical statisticians to develop new generalizations of distributions. The New Generalized Fisk distribution, a unique distribution presented in this study, is thoroughly examined. There is a thorough discussion of a few fundamental statistical traits and attributes, such as the quantile function, order statistics, skewness and kurtosis, moments, and moment-generating functions. The new distribution incorporates additional parameters, enhancing its ability to capture a wide range of skewness and kurtosis behaviors, making it applicable to diverse fields such as economics, reliability engineering, and environmental sciences. Both numerical and graphical evaluations are used to evaluate the performance of the recently proposed model. Additionally, the performance of the maximum likelihood estimators is assessed by a simulation study. Real-world applications are analyzed, and the model parameters are estimated using the maximum likelihood estimation technique. It is contrasted with the popular models of computing. According to model adequacy and discrimination approaches, the suggested model performs the best. The models are compared to choose the model that best fits the data with the essential characteristics. The graphical and model comparison approaches suggested an outstanding improvement in the combined distribution.