The Annals of Mathematical Statistics

A Multivariate Tchebycheff Inequality

Ingram Olkin and John W. Pratt

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Abstract

A multivariate Tchebycheff inequality is given, in terms of the covariances of the random variables in question, and it is shown that the inequality is sharp, i.e., the bound given can be achieved. This bound is obtained from the solution of a certain matrix equation and cannot be computed easily in general. Some properties of the solution are given, and the bound is given explicitly for some special cases. A Less sharp but easily computed and useful bound is also given.

Article information

Source
Ann. Math. Statist. Volume 29, Number 1 (1958), 226-234.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177706720

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177706720

Mathematical Reviews number (MathSciNet)
MR93865

Zentralblatt MATH identifier
0085.35204

Citation

Olkin, Ingram; Pratt, John W. A Multivariate Tchebycheff Inequality. The Annals of Mathematical Statistics 29 (1958), no. 1, 226--234. doi:10.1214/aoms/1177706720. http://projecteuclid.org/euclid.aoms/1177706720.


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