The gamma-order generalized Chi-gamma distribution

Accepted - June 2024

Abstract

The various attempts to present a generalized Normal distribution came to a conclusion by trial and error, rather than a theoretical framework. It is the γ-order Generalized Normal distribution with a strong theoretical background due to the Euclidean Logarithm Sobolev Inequality (LSI), adopting an extra, shape parameter. The introduced Generalized Gaussian offers extensions to the Information Theory oriented results among other applications. Based on this distribution we go a step forward to generalize the Chi-square distribution and we present in this paper the γ-order Generalized Chi-γ. Moreover, both Rayleigh and Maxwell–Boltzmann distributions have been generalized.