Advances and Applications in Statistics
Volume 2, Issue 2, Pages 131 - 137
(August 2002)
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SOME STUDY OF KURTOSIS: A NEW MEASURE OF PEAKEDNESS FOR DISTRIBUTIONS
Dane W. Wu (U. S. A.)
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Abstract: Kurtosis, or excess
coefficient, is commonly referred to the degree of
peakedness of a distribution. In the literature,
there are various criticisms on the inconsistency of
kurtosis in measuring the peakedness of a
distribution [J. Amer. Stat. Assoc. 69 (1974),
543-545; Comm. Stat. -Theory Meth. 16 (1987),
579-592; The Amer. Stat. 24 (1970), 19-22]. Several
alternative measures of peakedness were proposed
[The Amer. Stat. 37 (1983), 55-56; The Amer. Stat.
41 (1987), 1-5]. Through extensive study of kurtosis
on numerous distributions, this author introduces a
new measure of peakedness called w-peakedness
that is proved to have some nice properties. This
new measure can also be useful in estimating
multimodal densities [D. W. Wu, Estimation of
multimodal densities, Proceedings of the
Mathematical Modeling Symposium, University of
Wisconsin, U.S.A. (1999), 221-229]. |
Keywords and phrases: kurtosis, distribution, w-peakedness. |
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