| Title:
|
Bound on extended $f$-divergences for a variety of classes (English) |
| Author:
|
Cerone, Pietro |
| Author:
|
Dragomir, Sever S. |
| Author:
|
Österreicher, Ferdinand |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
6 |
| Year:
|
2004 |
| Pages:
|
[745]-756 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of $f$-divergences was introduced by Csiszár in 1963 as measures of the ‘hardness’ of a testing problem depending on a convex real valued function $f$ on the interval $[0,\infty )$. The choice of this parameter $f$ can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of $f$-divergences are given and the class of $\chi ^{\alpha }$-divergences is presented. Ostrowski’s inequality and a Trapezoid inequality are utilized in order to prove bounds for an extension of the set of $f$-divergences. The class of $\chi ^{\alpha }$-divergences and four further classes of $f$-divergences are used in order to investigate limitations and strengths of the inequalities derived. (English) |
| Keyword:
|
$f$-divergences |
| Keyword:
|
bounds |
| Keyword:
|
Ostrowki’s inequality |
| MSC:
|
62B10 |
| MSC:
|
62E99 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 1244.62005 |
| idMR:
|
MR2120395 |
| . |
| Date available:
|
2009-09-24T20:05:54Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135631 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
