R\'enyi entropy and complexity measure for skew-gaussian distributions and related families

TL;DR

This paper derives closed-form expressions for Rényi entropy and complexity measures for skew-gaussian distributions and related families, enhancing understanding of their informational properties.

Contribution

It introduces new closed-form formulas for Rényi entropy of skew-gaussian and extended skew-gaussian distributions, including inequalities and estimation methods.

Findings

Closed-form Rényi entropy expressions for skew-gaussian distributions.

Derived inequalities for Rényi and Shannon entropies.

Application of weighted moments estimation method.

Abstract

In this paper, we provide the R\'enyi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed expressions considering a more general class of closed skew-gaussian distributions and the weighted moments estimation method. In addition, closed expressions of R\'enyi entropy are presented for extended skew-gaussian and truncated skew-gaussian distributions. Finally, additional inequalities for skew-gaussian and extended skew-gaussian R\'enyi and Shannon entropies are reported.