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One-Sided Chebyshev Inequality

The one-sided Chebyshev inequality, also called Cantelli's inequality, states that a random variable X with finite mean mu and variance sigma^2 satisfies

P(X-mu>=a)<=(sigma^2)/(sigma^2+a^2)
(1)
P(X-mu<=-a)<=(sigma^2)/(sigma^2+a^2),
(2)

for a>0. Unlike the ordinary Chebyshev inequality, it bounds either tail separately.

See also

Chebyshev Inequality, Markov's Inequality, Variance

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References

Casella, G. and Berger, R. L. Statistical Inference, 2nd ed. Pacific Grove, CA: Duxbury, 2002.

Cite this as:

Weisstein, Eric W. "One-Sided Chebyshev Inequality." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/One-SidedChebyshevInequality.html

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