Extended inequalities for weighted Renyi entropy involving generalized Gaussian densities

Abstract: In this paper the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\alpha$-th generalized derivation and ($\alpha$; p)-th weighted Fisher information, extended versions of the moment-entropy, Fisher information and Cramer-Rao inequalities in terms of generalized Gaussian densities are given.