Basic inequalities for weighted entropies

被引：15

作者：

Suhov, Yuri ^{[1
,2
,3
]}

Stuhl, Izabella ^{[4
,5
,6
]}

Sekeh, Salimeh Yasaei ^{[7
]}

Kelbert, Mark ^{[8
,9
]}

机构：

[1] Univ Cambridge, DPMMS, Cambridge, England

[2] Penn State Univ, Dept Math, Philadelphia, PA USA

[3] IPIT RAS, Moscow, Russia

[4] Univ Sao Paulo, IMS, Sao Paulo, SP, Brazil

[5] Univ Denver, Dept Math, Denver, CO 80208 USA

[6] Univ Debrecen, Debrecen, Hungary

[7] Univ Fed Sao Carlos, Dept Stat, Sao Carlos, SP, Brazil

[8] Univ Swansea, Dept Math, Swansea, W Glam, Wales

[9] Moscow Higher Sch Econ, Moscow, Russia

来源：

AEQUATIONES MATHEMATICAE | 2016年 / 90卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

Weighted entropy; weighted conditional entropy; weighted relative entropy; weighted mutual entropy; weighted Gibbs inequality; convexity; concavity; weighted Hadamard inequality; weighed Fisher information; weighed Cramer-Rao inequalities; QUANTITATIVE-QUALITATIVE MEASURE; INFORMATION; DISTRIBUTIONS; SYSTEMS;

D O I：

10.1007/s00010-015-0396-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cram,r-Rao inequalities involving the weighted Fisher information matrix.

引用

页码：817 / 848

页数：32

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