Cantelli's inequality
id:
cantelli-s-inequality-189-14713127
title:
Cantelli's inequality
text:
In probability theory, Cantelli's inequality is an improved version of Chebyshev's inequality for one-sided tail bounds. The inequality states that, for λ > 0,
- Pr ≤ σ 2 σ 2 + λ 2, where
- X is a real-valued random variable,
- Pr is the probability measure,
- E [ X ] is the expected value of X,
- σ 2 is the variance of X. Applying the Cantelli inequality to − X gives a bound on the lower tail,
- Pr ≤ σ 2 σ 2 + λ 2. While the inequality is often attributed to Francesco Paolo Cantelli
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Cantelli%27s_inequality
date created:
2012-08-12T16:58:27Z
date modified:
2024-09-09T16:48:35Z
main entity:
{"identifier":"Q3711841","url":"https://www.wikidata.org/entity/Q3711841"}
image:
fields total:
13
integrity:
14