Azuma's inequality

en

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Azuma's inequality

Quality:

Azuma's inequality - probabilistic inequality applying to martingales with bounded differences. Article “Azuma's inequality” in English Wikipedia has 21 points for quality (as of July 1, 2025). The article contains 1 references and 11 sections.

This article has the best quality in Chinese Wikipedia. However, this article is the most popular in English version.

Since the creation of article “Azuma's inequality”, its content was written by 49 registered users of English Wikipedia and edited by 85 registered Wikipedia users in all languages.

The article is cited 22 times in English Wikipedia and cited 40 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #24979 in February 2004
  • Global: #49999 in February 2004

The highest popularity rank from 2008:

  • Local (English): #361442 in February 2008
  • Global: #566354 in April 2018

There are 6 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1Chinese (zh)
吾妻不等式
22.1216
2English (en)
Azuma's inequality
20.9916
3German (de)
Ungleichung von Azuma-Hoeffding
18.1766
4Russian (ru)
Неравенство Азумы
15.4956
5French (fr)
Inégalité d'Azuma
13.4341
6Vietnamese (vi)
Bất đẳng thức Azuma
5.6681
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Azuma's inequality" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Azuma's inequality
344 400
2French (fr)
Inégalité d'Azuma
24 521
3Vietnamese (vi)
Bất đẳng thức Azuma
21 595
4Chinese (zh)
吾妻不等式
11 351
5Russian (ru)
Неравенство Азумы
2 533
6German (de)
Ungleichung von Azuma-Hoeffding
760
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Azuma's inequality" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Azuma's inequality
1 853
2French (fr)
Inégalité d'Azuma
102
3Chinese (zh)
吾妻不等式
96
4German (de)
Ungleichung von Azuma-Hoeffding
65
5Vietnamese (vi)
Bất đẳng thức Azuma
47
6Russian (ru)
Неравенство Азумы
36
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Azuma's inequality" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Azuma's inequality
49
2French (fr)
Inégalité d'Azuma
23
3Vietnamese (vi)
Bất đẳng thức Azuma
6
4German (de)
Ungleichung von Azuma-Hoeffding
3
5Chinese (zh)
吾妻不等式
3
6Russian (ru)
Неравенство Азумы
1
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Azuma's inequality" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Ungleichung von Azuma-Hoeffding
0
2English (en)
Azuma's inequality
0
3French (fr)
Inégalité d'Azuma
0
4Russian (ru)
Неравенство Азумы
0
5Vietnamese (vi)
Bất đẳng thức Azuma
0
6Chinese (zh)
吾妻不等式
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Azuma's inequality" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Azuma's inequality
22
2French (fr)
Inégalité d'Azuma
7
3Chinese (zh)
吾妻不等式
5
4Vietnamese (vi)
Bất đẳng thức Azuma
4
5Russian (ru)
Неравенство Азумы
2
6German (de)
Ungleichung von Azuma-Hoeffding
0
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Ungleichung von Azuma-Hoeffding
enEnglish
Azuma's inequality
frFrench
Inégalité d'Azuma
ruRussian
Неравенство Азумы
viVietnamese
Bất đẳng thức Azuma
zhChinese
吾妻不等式

Popularity rank trends

Best Rank English:
#361442
02.2008
Global:
#566354
04.2018

AI rank trends

Best Rank English:
#24979
02.2004
Global:
#49999
02.2004

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Azuma's inequality from Wikipedia articles about Hoeffdings inequality, Inequality, Martingale, McDiarmids inequality and Bernstein inequalities. Whereas reading the article about Azuma's inequality people most often go to Wikipedia articles on Martingale, Kazuoki Azuma, Concentration inequality, Hoeffdings lemma and Wassily Hoeffding.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 10 February 2026

On 10 February 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: Jeffrey Epstein, Ghislaine Maxwell, Ilia Malinin, Bad Bunny, 2026 Winter Olympics, Epstein files, Jutta Leerdam, Jake Paul, Puerto Rico, Little Saint James.

In English Wikipedia the most popular articles on that day were: Bad Bunny, Jeffrey Epstein, Epstein files, Ilia Malinin, Savannah Guthrie, Ghislaine Maxwell, 2026 Winter Olympics, List of Super Bowl halftime shows, Eileen Gu, Jutta Leerdam.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information