Open Access
June, 1948 An Inequality for Kurtosis
Louis Guttman
Ann. Math. Statist. 19(2): 277-278 (June, 1948). DOI: 10.1214/aoms/1177730255


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.


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Louis Guttman. "An Inequality for Kurtosis." Ann. Math. Statist. 19 (2) 277 - 278, June, 1948.


Published: June, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0031.36901
MathSciNet: MR25105
Digital Object Identifier: 10.1214/aoms/1177730255

Rights: Copyright © 1948 Institute of Mathematical Statistics

Vol.19 • No. 2 • June, 1948
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