Gamma-order Generalized Normal distribution

Gamma-Ordered Generalized Normal Distribution

The multivariate Normal distribution, [1], is extended due to the Logarithmic Sobolev Inequalities (LSI), [2], and can act as a family of distributions based on a “shape” parameter. This shape parameter $\gamma \in \mathbb {R} -[0,1]$ creates along with parameters of position, $\mu \in \mathbb {R} ^{p}$, and dispersion, $\Sigma \in \mathbb {R} ^{p\times p}$, the $N_{\gamma }(\mu ,\Sigma )$ family of distributions with probability density function, [3]