The Case for Shifting the Rényi Entropy
We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications.
| Medienart: |
E-Artikel |
|---|
| Erscheinungsjahr: |
2019 |
|---|---|
| Erschienen: |
2019 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:21 |
|---|---|
| Enthalten in: |
Entropy (Basel, Switzerland) - 21(2019), 1 vom: 09. Jan. |
| Sprache: |
Englisch |
|---|
| Beteiligte Personen: |
Valverde-Albacete, Francisco J [VerfasserIn] |
|---|
| Links: |
|---|
| Themen: |
Escort distributions |
|---|
| Anmerkungen: |
Date Revised 29.03.2024 published: Electronic Citation Status PubMed-not-MEDLINE |
|---|
| doi: |
10.3390/e21010046 |
|---|
| funding: |
|
|---|---|
| Förderinstitution / Projekttitel: |
|
| PPN (Katalog-ID): |
NLM31832945X |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | NLM31832945X | ||
| 003 | DE-627 | ||
| 005 | 20240330000045.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 231225s2019 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.3390/e21010046 |2 doi | |
| 028 | 5 | 2 | |a pubmed24n1355.xml |
| 035 | |a (DE-627)NLM31832945X | ||
| 035 | |a (NLM)33266762 | ||
| 035 | |a (PII)E46 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Valverde-Albacete, Francisco J |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The Case for Shifting the Rényi Entropy |
| 264 | 1 | |c 2019 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ƒaComputermedien |b c |2 rdamedia | ||
| 338 | |a ƒa Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Date Revised 29.03.2024 | ||
| 500 | |a published: Electronic | ||
| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Hölder means | |
| 650 | 4 | |a Shannon-type relations | |
| 650 | 4 | |a escort distributions | |
| 650 | 4 | |a generalized weighted means | |
| 650 | 4 | |a shifted Rényi entropy | |
| 700 | 1 | |a Peláez-Moreno, Carmen |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Entropy (Basel, Switzerland) |d 2008 |g 21(2019), 1 vom: 09. Jan. |w (DE-627)NLM191572098 |x 1099-4300 |7 nnns |
| 773 | 1 | 8 | |g volume:21 |g year:2019 |g number:1 |g day:09 |g month:01 |
| 856 | 4 | 0 | |u http://dx.doi.org/10.3390/e21010046 |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a GBV_NLM | ||
| 951 | |a AR | ||
| 952 | |d 21 |j 2019 |e 1 |b 09 |c 01 | ||