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Entropy of Degree s and its Multivariate Cases

We know that the entropy of degree $s$ i.e., unified $(s,s)-$entropy is given by

$${\ensuremath{\boldsymbol{\mathscr{H}}}}^s_s(X)=\left\{\begin{arra...... 1 \\ H(X) = - \sum_{i=1}^n p(x_i)\, log \,p(x_i), & s=1\end{array}\right.$$

In the following subsection we shall present the four different ways of writing conditional entropies of degree$s$.