The Annals of Mathematical Statistics

An Inequality for Kurtosis

Louis Guttman

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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


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