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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 657-668, October 2007




THE EFFECT OF THE SKEWING DISTRIBUTION ON

SKEW-SYMMETRIC FAMILIES


BY


DALE UMBACH




Abstract. Skew-symmetric families of distributions are perturbed distributions about a central symmetric distribution, the kernel. Another distribution, the skewing distribution, is used to generate perturbations of the kernel which produces a family of distributions with the kernel as a central member of the family. In this note, it is argued that the choice of skewing distribution does not have a major effect on the shape of the distributions in the ensuing family.

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Received February 13, 2006; revised March 21, 2007.

AMS Subject Classification. 60E05, 62E17.

Key words. shape, skewing distribution, skew-symmetric distributions.