## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 29, Number 1 (1958), 1-350

### A Multivariate Tchebycheff Inequality

Ingram Olkin and John W. Pratt

#### 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: 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.