In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation...
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first Chebyshev inequality, while referring to Chebyshev's inequality as the second Chebyshev inequality) or Bienaymé's inequality. Markov's inequality (and...
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probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of...
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Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for...
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In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if a 1 ≥ a 2 ≥ ⋯ ≥ a n {\displaystyle a_{1}\geq a_{2}\geq \cdots...
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between n and 2n. Chebyshev's inequality, on the range of standard deviations around the mean, in statistics Chebyshev's sum inequality, about sums and...
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the Chebyshev inequality (which can be used to prove the weak law of large numbers), the Bertrand–Chebyshev theorem, Chebyshev polynomials, Chebyshev linkage...
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\Phi (a))\leq {\frac {\operatorname {E} (\Phi (X))}{\Phi (a)}}.} Chebyshev's inequality requires the following information on a random variable X {\displaystyle...
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Chernoff bound (redirect from Chernoff's inequality)
Markov's inequality or Chebyshev's inequality. The Chernoff bound is related to the Bernstein inequalities. It is also used to prove Hoeffding's inequality, Bennett's...
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Standard deviation (section Chebyshev's inequality)
Accuracy and precision Algorithms for calculating variance Chebyshev's inequality An inequality on location and scale parameters Coefficient of variation...
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inequality follows by Chebyshev's inequality. This inequality was generalized by Hájek and Rényi in 1955. Chebyshev's inequality Etemadi's inequality...
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unimodality Chebyshev's inequality would give a looser bound of 1/9 = 0.11111.... An improved version of the Vysochanskij-Petunin inequality for one-sided...
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several more general laws of large numbers in probability theory. Chebyshev's inequality. Let X be a random variable with finite expected value μ and finite...
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the Chebyshev–Markov–Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and...
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inequalities Chebyshev's bias Chebyshev's inequality in probability and statistics Chebyshev–Cantelli inequality Multidimensional Chebyshev's inequality...
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inequality Chebyshev–Markov–Stieltjes inequalities Chebyshev's sum inequality Clarkson's inequalities Eilenberg's inequality Fekete–Szegő inequality Fenchel's...
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Expected value (section Inequalities)
and Chebyshev inequalities often give much weaker information than is otherwise available. For example, in the case of an unweighted dice, Chebyshev's inequality...
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{n-1}{\sqrt {n}}}.} Chebyshev's inequality locates a certain fraction of the data within certain bounds, while Samuelson's inequality locates all the data...
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(about 4.5 for 95% confidence). Cantelli's inequality is the one-tailed version of Chebyshev's inequality. Binomial proportion confidence interval Rule...
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Vysochanskiï–Petunin inequality, a similar result for the distance from the mean rather than the mode Chebyshev's inequality, concerns distance from...
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Concentration inequality - a summary of tail-bounds on random variables. Hoeffding's inequality S.N.Bernstein, "On a modification of Chebyshev's inequality and...
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Azuma's inequality Bernoulli's inequality Bell's inequality Boole's inequality Cauchy–Schwarz inequality Chebyshev's inequality Chernoff's inequality Cramér–Rao...
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Doob martingale (redirect from McDiarmid’s Inequality)
the central limit theorem, law of large numbers, Chernoff's inequality, Chebyshev's inequality or similar tools. When analyzing similar objects where the...
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модификациях неравенства Чебышёва [On certain modifications of Chebyshev's inequality]. Doklady Akademii Nauk SSSR (in Russian). 17 (6): 275–277. (vol...
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(in which case it is known as Markov inequality), or the quadratic function (respectively Chebyshev's inequality). Another useful result is the continuous...
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polynomials Chebyshev filter Chebyshev's inequality Chebyshev distance Chebyshev (crater): A lunar crater 2010 Chebyshev: An asteroid from the asteroid...
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qualify as a discovery. A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least...
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relation holds uniformly in x, which can be seen from its proof via Chebyshev's inequality, taking into account that the variance of 1⁄n K, equal to 1⁄n x(1−x)...
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polynomials Chebyshev rational functions Approximation theory The Chebfun system Discrete Chebyshev transform Markov brothers' inequality Clenshaw algorithm...
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Characteristic function (probability theory) Chauvenet's criterion Chebyshev center Chebyshev's inequality Checking if a coin is biased – redirects to Checking whether...
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