On the Emerged from LSI γ-Order Generalized Normal Distribution

The target of this paper is to provide evidence that the γ γ -order Generalized Normal distribution emerged from the Logarithmic Sobolev Inequalities is the only one based on a strong solid theoretical background, while the existing similar attempts lack theoretical basis. Moreover, the theoretical extensions provided by this distribution create new γ γ -order distributions, fit to the Information Theory and provide more Statistical and Mathematical extensions.