The Annals of Mathematical Statistics

An Inequality for Kurtosis

Louis Guttman

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

First available in Project Euclid: 28 April 2007

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

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