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ⓘ Bhatia–Davis inequality. In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ 2 of a ..




                                     

ⓘ Bhatia–Davis inequality

In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ 2 of any bounded probability distribution on the real line.

Suppose a distribution has minimum m, maximum M, and expected value μ. Then the inequality says:

σ 2 ≤ M − μ − m. {\displaystyle \sigma ^{2}\leq M-\mu\mu -m.\,}

Equality holds precisely if all of the probability is concentrated at the endpoints m and M.

The Bhatia–Davis inequality is stronger than Popovicius inequality on variances.

                                     
  • geometry and matrix analysis. He is one of the eponyms of the Bhatia Davis inequality Rajendra Bhatia founded the series Texts and Readings in Mathematics in
  • specified amount Bhatia Davis inequality an upper bound on the variance of any bounded probability distribution Bernstein inequalities probability theory
  • He is one of the eponyms of the Davis Kahan theorem and Bhatia Davis inequality along with Rajendra Bhatia The Davis Kahan Weinberger dilation theorem
  • Entropy, doi: 10.3390 e16063273. Bhatia R. Davis C. 1993 More matrix forms of the arithmetic - geometric mean inequality SIAM Journal on Matrix Analysis
  • many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with
  • inequality  F: R Bernstein inequalities F: R Bhatia Davis inequality Chernoff bound  F: B Doob s martingale inequality FU: R Dudley s theorem 
  • distribution Beta rectangular distribution Beverton Holt model Bhatia Davis inequality Bhattacharya coefficient  redirects to Bhattacharyya distance
  • portal Average absolute deviation Bhatia Davis inequality Common - method variance Correlation Chebyshev s inequality Distance variance Estimation of covariance
  •  2071. Attwood 2005. Srivastava 1968. Sen 1982. Bhatia 1985. Mander 2009, p. 1. Davis 2001, p. 299. Davis 2001, pp. 299 300. Wong 1998. Martin Ravallion
  • Money and Power: How Goldman Sachs Came to Rule the World 2012 Gauri Bhatia Here s how India s wealthiest families are seeking to stay wealthy, CNBC