Heavy Tailed Distribution of Binary Classification Model

The proposed research incorporates the utilization of a heavy-tailed skewed distribution referred to as the inverse Weibull as a link function in the context of a binary classification model. This selection is motivated by the need to address the existence of rare or extreme events in random processes. The study introduces a model that relies on the Inverse Weibull (TYPE II) distribution, and the estimation of model parameters is accomplished through the application of maximum likelihood methods. When the outcomes are compared to those derived from other link functions such as TYPE I (Complementary log) and TYPE III (Weibull) based on extreme value distributions using standard classification data as well as real-life data, it becomes apparent that the Inverse Weibull (TYPE II) model exhibits exceptional performance. This assessment of performance takes into account several criteria, encompassing the Akaike information criterion, Bayesian information criterion, Area under the curve, and Brier scores. In conclusion, the study establishes that the proposed model demonstrates considerable robustness in its performance, rendering it a viable choice for the modeling of binary classification problems.