On the Maximum of the Standardized Fourth Moment
by Robert H. Byers, Jr
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) .
kurtosis, skewness, moments
Robert H. Byers, Jr.,
READING THE ARTICLE: You can read the article in
portable document (.pdf) format (47325 bytes.)
NOTE: The content of this article is the intellectual property of the authors, who retains all rights to future publication.
This page has been accessed times since .
Return to the Home Page.