MLE for the γ-order generalized Normal distribution

Abstract

The introduced three parameter (position �, scaleand shape ) mul- tivariate generalized Normal distribution (-GND) is based on a strong the- oretical background and emerged from Logarithmic Sobolev Inequalities. It includes a number of well known distributions such as the multivariate Uni- form, Normal, Laplace and the degenerated Dirac distributions. In this pa- per, the cumulative distribution, the truncated distribution and the hazard rate of the -GND are presented. In addition, the Maximum Likelihood Es- timation (MLE) method is discussed in both the univariate and multivariate cases and asymptotic results are presented.