Extended inequalities for weighted Renyi entropy involving generalized Gaussian densities

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.Comment: 17 page

Simple inequalities for weighted entropies

A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.Comment: 19 pages The paper is wihdrawn as it needs improvemen

Basic inequalities for weighted entropies

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of the weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cram\'{e}r-Rao inequalities involving the weighted Fisher information matrix.Comment: arXiv admin note: substantial text overlap with arXiv:1409.410