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Cantelli One-Sided Probability Bound Calculator

P(X ≥ μ + k·σ) ≤ 1/(1+k²) — one-sided Chebyshev.

Applies the Cantelli inequality: P(X − μ ≥ kσ) ≤ 1/(1+k²), a tighter one-sided bound than Chebyshev. Also computes the two-sided Chebyshev bound P(|X−μ| ≥ kσ) ≤ 1/k².

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

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Formula

P(X ≥ μ+kσ) ≤ 1/(1+k²) [Cantelli]; P(|X−μ|≥kσ) ≤ 1/k² [Chebyshev]

In depth

Applies the Cantelli inequality: P(X − μ ≥ kσ) ≤ 1/(1+k²), a tighter one-sided bound than Chebyshev. Also computes the two-sided Chebyshev bound P(|X−μ| ≥ kσ) ≤ 1/k².