On the Maximum of the Standardized Fourth Moment

by Robert H. Byers, Jr .

Abstract: For sample size n it is known that the kurtosis statistic b2 (the standardized fourth moment) is less than or equal to n. We show that the upper bound on b2 is n - 2 + 1/(n-1), and that this maximum will be reached when n - 1 of the data points are equal to each other and unequal to the n-th point. The skewness statistic also has a maximum when the data are so arranged, and it is n - 3 + 1/(n - 1) .

Key Words: kurtosis, skewness, moments

Authors:
Robert H. Byers, Jr., rhb1@cdc.gov

Editor: Wei-Min Huang , wh02@lehigh.edu

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