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Activity Number:
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149
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Type:
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Contributed
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Date/Time:
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Monday, July 30, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #308901 |
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Title:
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A Family of Kurtosis Orderings for Multivariate Distributions
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Author(s):
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Jin Wang*+
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Companies:
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Northern Arizona University
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Address:
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Department of Mathematics and Statistics, Flagstaff, AZ, 86011-5717,
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Keywords:
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Kurtosis ; Peakedness ; Tailweight ; Ordering ; Elliptically symmetric distributions ; Multivariate analysis
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Abstract:
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Extending the van Zwet (1964) kurtosis ordering for univariate symmetric distributions, we define and study a family of kurtosis orderings for multivariate distributions. All those orderings are affine invariant and that a distribution F is less than or equal to a distribution G in each ordering implies that G has at least as much peakedness and at least as much tailweight as F. All even moments of the Mahalanobis distance of a random vector (if exist) preserve some set of the orderings. For elliptically symmetric distributions, each ordering determines the distribution up to affine equivalence. Ordering results are established for three important families of elliptically symmetric distributions: Kotz type distributions, Pearson Type VII distributions, and Pearson Type II distributions. Finally application to assess multivariate normality is discussed.
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