Weighted Approach to Rényi Entropy

Abstract: R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the R\'enyi entropy dimension of arbitrary order of a mixture of measures. The key for obtaining these results is our new definition of the weighted R\'enyi entropy. It is shown that weighted entropy is equal to the classical R\'enyi entropy.