Rènyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting

We study nonextensive statistical scenarios à la Tsallis with reference to Fisher’s information and Rènyi’s entropy. A new way of evaluating Tsallis’ generalized expectation values is examined within such a context, and is shown to lead to a much better Cramer–Rao bound than the customary procedure. A connection between the information measures of Fisher’s and Rènyi’s is found. We show that Fisher’s measure for translation families remains additive even in a non-extensive Tsallis setting.