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$q$-deformations of fundamental equation of information and entropies

$q$-deformations of Shannon entropy Let $q\in\mathbb R-\{1\}$ and $x>0$. … x \ln_q \frac{1}{x}+ (1-x)\ln_q \frac{1}{1-x} $$ and the $q$-Rényi entropy $$R_q(x)= \ln e_q(S_q(x)). $$ Both $q$ entropies are deformations of Shannon entropy, as $$\lim_{q\rightarrow 1}S_q(x)=\lim …
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Higher moments of information and Renyi entropy

Matthews, "Entropy and Higher Moments of Information", Journal of Universal Computer Science vol 16, nr. 5 (2010) which is available here, the authors introduce the higher moments of information of memoryless … They move from the Shannon entropy formalism to more general entropies in section 7. …
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