Bhatia–Davis inequality

Template:Primary sources In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ² 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:

$\sigma ^{2}\leq (M-\mu )(\mu -m).\,$

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

The Bhatia–Davis inequality is stronger than Popoviciu's inequality on variances.

See also

• Cramér–Rao bound
• Chapman–Robbins bound

References

• Template:Cite journal

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