In probability theory, concentration inequalities provide mathematical bounds on the probability of a random variable deviating from some value (typically...

various members or groups in a society. It shows one aspect of economic inequality or economic heterogeneity. The distribution of wealth differs from the...

probability theory field of mathematics, Talagrand's concentration inequality is an isoperimetric-type inequality for product probability spaces. It was first...

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...

In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation...

mathematical inequalities. Agmon's inequality Askey–Gasper inequality Babenko–Beckner inequality Bernoulli's inequality Bernstein's inequality (mathematical...

{\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...

Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for...

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...

Loomis–Whitney inequality and Hölder's inequality. The second is a result of probability theory which gives a concentration inequality for log-concave...

inequalities Concentration inequality − a summary of tail-bounds on random variables. Cramér's theorem Entropic value at risk Hoeffding's inequality Matrix...

theoretical computer science, McDiarmid's inequality (named after Colin McDiarmid ) is a concentration inequality which bounds the deviation between the...

developed nations. However, the inequality indicators vary considerably from state to state. States that have a high concentration of skilled jobs, implement...

using Hölder's inequality in place of the Cauchy-Schwarz inequality. Cantelli's inequality Second moment method Concentration inequality – a summary of...

Bernstein inequalities are also known as the Chernoff bound, Hoeffding's inequality and Azuma's inequality. The martingale case of the Bernstein inequality is...

Rademacher variables, including concentration inequalities such as Bernstein inequalities as well as anti-concentration inequalities like Tomaszewski's conjecture...

new aspects of the isoperimetric and concentration of measure phenomena for product spaces, by obtaining inequalities which make use of new kinds of distances...

Economic inequality is an umbrella term for three concepts: income inequality, how the total sum of money paid to people is distributed among them; wealth...

Prékopa–Leindler inequality is an integral inequality closely related to the reverse Young's inequality, the Brunn–Minkowski inequality and a number of...

{\frac {t}{np}}))} . Concentration inequality - a summary of tail-bounds on random variables. Bennett, G. (1962). "Probability Inequalities for the Sum of Independent...

Causes of inequality may include executive compensation increasing relative to the average worker, financialization, greater industry concentration, lower...

}}\varepsilon ={\sqrt {\frac {\ln {\frac {2}{\alpha }}}{2n}}}.} Concentration inequality – a summary of bounds on sets of random variables. Dvoretzky, A...

probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales...

concerns distance from the mean without requiring unimodality Concentration inequality – a summary of tail-bounds on random variables. Winkler A. (1886)...

Dvoretzky–Kiefer–Wolfowitz inequality, the Bousquet inequality, the concentration inequality, and the Efron-Stein inequality. With Lucien Birgé he worked...

impacts. Dynasty trusts have become a focal point in debates about wealth inequality and economic mobility. Critics argue that by enabling vast fortunes to...

wealth inequality in his work On the measurement of concentration and variability of characters in 1914. Here, he presented the concentration ratio, which...

Social inequality occurs when resources within a society are distributed unevenly, often as a result of inequitable allocation practices that create distinct...

on hypothesis testing　 (Bretagnolle–Huber–Carol Inequality is a variation of Concentration inequality for multinomially distributed random variables which...

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...