The Rényi entropy function was optimized for the novel findings of this investigation under various conditions. Their research's findings suggest that generalized t-distributions cover the complete spectrum of Lévy stable distributions. Additionally, an exposition was undertaken to prove that the Lévy distribution generalizes the Tsallisian distribution rather than the reverse. The current study is a strong generalization of an existing research work in the literature. Notable entropic applications to machine learning are addressed. Concluding remarks are given, combined with some strong open problems and future research pathways.