We study nonextensive statistical scenarios a la Tsallis with referenc
e to Fisher's information and Renyi's entropy. A new way of evaluating
Tsallis' generalized expectation values is examined within such a con
text, 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 Renyi's is found. We show that Fisher's measure for trans
lation families remains additive even in a non-extensive Tsallis setti
ng. (C) 1998 Elsevier Science B.V. All rights reserved.