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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