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KULLBACK-LEIBLER DIVERGENCE FOR THE $\gamma$-ORDER GENERALIZED NORMAL $ N_\gamma\left(\mu, \sigma^2\right) $
Keywords:
$\gamma$-order Generalized Normal distribution, Kullback-Leibler divergence, entropy power.DOI:
https://doi.org/10.17654/0972086325003Abstract
The target of this paper is to discuss the Kullback-Leibler divergence for the family of $\gamma$-order Generalized Normal distribution. It has emerged from the Euclidean Logarithmic Sobolev Inequality and due to an "extra" shape parameter is an extension for the multivariate Normal distribution. In particular, for different $\gamma$-orders and variances, the corresponding divergences are evaluated. The evaluated results coincide with the existing ones, in the case of $\gamma=2$, the classical Normal case.
Received: November 1, 2024
Accepted: December 10, 2024
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