Renyi Entropy

$H_{\alpha }(X)=\frac{1}{1-\alpha }\log \left({\sum }_i{p}_i^{\alpha }\right)$, where

• $X$ is a discrete Random variable
• $\alpha \in {\mathbb{R}}^{+}$
• $p_i$ is the probability of event $i$.

Remark: $H_{\alpha }$ for $\alpha \in \{0,1,\infty \}$, is defined by taking the limit $H_{\alpha }={\lim }_{\gamma \to \alpha }{H}_{\gamma }$.