• In probability theory, concentration inequalities provide mathematical bounds on the probability of a random variable deviating from some value (typically...
    18 KB (3,126 words) - 23:13, 2 September 2024
  • probability theory field of mathematics, Talagrand's concentration inequality is an isoperimetric-type inequality for product probability spaces. It was first...
    3 KB (518 words) - 08:43, 10 April 2024
  • Thumbnail for Distribution of wealth
    various members or groups in a society. It shows one aspect of economic inequality or economic heterogeneity. The distribution of wealth differs from the...
    77 KB (5,998 words) - 14:09, 8 July 2024
  • theoretical computer science, McDiarmid's inequality (named after Colin McDiarmid ) is a concentration inequality which bounds the deviation between the...
    17 KB (3,761 words) - 09:54, 29 July 2024
  • Hoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's...
    13 KB (2,351 words) - 19:50, 20 August 2024
  • {\displaystyle \sigma _{n}(S^{n})=1} ), one can deduce the following concentration inequality: σ n ( A ϵ ) ≥ 1 − C exp ⁡ ( − c n ϵ 2 ) {\displaystyle \sigma...
    10 KB (1,392 words) - 18:46, 13 January 2024
  • In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some...
    14 KB (2,520 words) - 17:18, 27 September 2024
  • Loomis–Whitney inequality and Hölder's inequality. The second is a result of probability theory which gives a concentration inequality for log-concave...
    13 KB (2,384 words) - 23:48, 19 August 2024
  • mathematical inequalities. Agmon's inequality Askey–Gasper inequality Babenko–Beckner inequality Bernoulli's inequality Bernstein's inequality (mathematical...
    9 KB (709 words) - 17:09, 6 October 2023
  • In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation...
    51 KB (7,513 words) - 22:12, 19 September 2024
  • Thumbnail for Social inequality
    Social inequality occurs when resources within a society are distributed unevenly, often as a result of inequitable allocation practices that create distinct...
    93 KB (11,145 words) - 21:46, 23 September 2024
  • inequalities Concentration inequality − a summary of tail-bounds on random variables. Cramér's theorem Entropic value at risk Hoeffding's inequality Matrix...
    32 KB (5,086 words) - 07:04, 1 September 2024
  • Rademacher variables, including concentration inequalities such as Bernstein inequalities as well as anti-concentration inequalities like Tomaszewski's conjecture...
    8 KB (997 words) - 09:42, 12 September 2024
  • Bernstein inequalities are also known as the Chernoff bound, Hoeffding's inequality and Azuma's inequality. The martingale case of the Bernstein inequality is...
    7 KB (1,382 words) - 02:46, 14 February 2024
  • probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales...
    11 KB (2,162 words) - 08:39, 22 May 2024
  • Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for...
    4 KB (649 words) - 16:48, 9 September 2024
  • using Hölder's inequality in place of the Cauchy-Schwarz inequality. Cantelli's inequality Second moment method Concentration inequality – a summary of...
    5 KB (849 words) - 11:52, 12 March 2023
  • Thumbnail for Michel Talagrand
    new aspects of the isoperimetric and concentration of measure phenomena for product spaces, by obtaining inequalities which make use of new kinds of distances...
    15 KB (1,424 words) - 18:31, 20 September 2024
  • Dvoretzky–Kiefer–Wolfowitz inequality, the Bousquet inequality, the concentration inequality, and the Efron-Stein inequality. With Lucien Birgé he worked...
    4 KB (235 words) - 02:57, 4 February 2024
  • Thumbnail for Economic inequality
    Wealth disparity in major cities Economic inequality is an umbrella term for a) income inequality or distribution of income (how the total sum of money...
    151 KB (15,534 words) - 10:41, 25 September 2024
  • {\frac {t}{np}}))} . Concentration inequality - a summary of tail-bounds on random variables. Bennett, G. (1962). "Probability Inequalities for the Sum of Independent...
    5 KB (681 words) - 19:15, 2 May 2024
  • on hypothesis testing  (Bretagnolle–Huber–Carol Inequality is a variation of Concentration inequality for multinomially distributed random variables which...
    9 KB (1,629 words) - 06:01, 15 May 2024
  • Thumbnail for Gini coefficient
    Gini coefficient (category Income inequality metrics)
    wealth inequality in his work On the measurement of concentration and variability of characters in 1914. Here, he presented the concentration ratio, which...
    95 KB (10,766 words) - 08:34, 27 August 2024
  • developed nations. However, the inequality indicators vary considerably from state to state. States that have a high concentration of skilled jobs, implement...
    32 KB (1,337 words) - 16:42, 3 December 2023
  • Prékopa–Leindler inequality is an integral inequality closely related to the reverse Young's inequality, the Brunn–Minkowski inequality and a number of...
    10 KB (1,160 words) - 23:21, 6 May 2023
  • Thumbnail for Dvoretzky–Kiefer–Wolfowitz inequality
    probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) provides a bound on the worst case distance of an empirically...
    9 KB (1,286 words) - 07:36, 13 May 2024
  • might not be. Chernoff's inequality Edgeworth series List of inequalities List of mathematical theorems Concentration inequality Since the random variables...
    14 KB (1,929 words) - 00:58, 26 May 2024
  • Thumbnail for Income inequality in the United States
    Causes of inequality may include executive compensation increasing relative to the average worker, financialization, greater industry concentration, lower...
    209 KB (20,973 words) - 15:36, 19 September 2024
  • ownership concentration was reported to be high even in areas where family farms are settled. This is a disturbing issue with regards to income inequality as...
    5 KB (578 words) - 16:43, 26 July 2024
  • McDiarmid's inequality. The Doob martingale was introduced by Joseph L. Doob in 1940 to establish concentration inequalities such as McDiarmid's inequality, which...
    6 KB (1,320 words) - 04:47, 1 January 2024