## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 19, Number 2 (1948), 277-278.

### An Inequality for Kurtosis

#### Abstract

It is well known that, if the fourth moment about the mean of a frequency distribution equals the square of the variance, then the frequencies are piled up at exactly two points, namely, the two points that are one standard deviation away from the mean. In this paper is developed a general inequality which describes the piling up of frequency around these two points for the case where the fourth moment exceeds the square of the variance. In a sense, it is shown how "U-shaped" a distribution must be according to its second and fourth moments.

#### Article information

**Source**

Ann. Math. Statist., Volume 19, Number 2 (1948), 277-278.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177730255

**Digital Object Identifier**

doi:10.1214/aoms/1177730255

**Mathematical Reviews number (MathSciNet)**

MR25105

**Zentralblatt MATH identifier**

0031.36901

**JSTOR**

links.jstor.org

#### Citation

Guttman, Louis. An Inequality for Kurtosis. Ann. Math. Statist. 19 (1948), no. 2, 277--278. doi:10.1214/aoms/1177730255. https://projecteuclid.org/euclid.aoms/1177730255