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Home > Art, Film & Photography > Statistical Inequalities: Chebyshev's Inequality, Jensen's Inequality, Cramr-Rao Bound, Kullback's Inequality, Doob's Martingale Inequality
Statistical Inequalities: Chebyshev's Inequality, Jensen's Inequality, Cramr-Rao Bound, Kullback's Inequality, Doob's Martingale Inequality

Statistical Inequalities: Chebyshev's Inequality, Jensen's Inequality, Cramr-Rao Bound, Kullback's Inequality, Doob's Martingale Inequality


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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Chebyshev's Inequality, Jensen's Inequality, Cramr-rao Bound, Kullback's Inequality, Doob's Martingale Inequality, Dvoretzky-kiefer-wolfowitz Inequality, Entropy Power Inequality, Vysochanski-petunin Inequality, Marcinkiewicz-zygmund Inequality, Boole's Inequality, le Cam's Theorem, Cheeger Bound, Mcdiarmid's Inequality, Samuelson's Inequality, Etemadi's Inequality, Multidimensional Chebyshev's Inequality, Fisher's Inequality, Bhatia-davis Inequality, Popoviciu's Inequality on Variances, Correlation Inequality. Excerpt: In mathematics, the Bhatia Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance of any bounded probability distribution on the real line. Suppose a distribution has minimum m, maximum M, and expected value . Then the inequality says: Equality holds precisely if all of the probability is concentrated at the endpoints m and M . The Bhatia Davis inequality is stronger than Popoviciu's inequality on variances . See also (online edition) References (URLs online) A hyperlinked version of this chapter is at In probability theory, Boole's inequality, named after George Boole, (also known as the union bound ) says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. Formally, for a countable set of events A 1, A 2, A 3, ..., we have In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure ) is -sub-additive. Bonferroni inequalities Boole's inequality may be generalised to find upper and lower bounds on the probability of finite unions of events. These bounds are known as Bonferroni inequalities, after Carlo Emilio Bonferroni ....


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Product Details
  • ISBN-13: 9781155281902
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Chebyshev's Inequality, Jensen's Inequality, Cramr-Rao Bound, Kullback's Inequality, Doob's Martingale Inequality
  • Width: 229 mm
  • ISBN-10: 115528190X
  • Publisher Date: 02 May 2010
  • Binding: Paperback
  • Spine Width: 4 mm
  • Weight: 109 gr


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