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Some moment relationships for multivariate skew-symmetric distributions

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  • Umbach, Dale

Abstract

Moments of multivariate skew-symmetric distributions which are generated from spherically symmetric and elliptically symmetric kernels are considered. For a rather general class of spherically symmetric kernels a strong relationship to the univariate case is established. This is exploited to demonstrate that the structure of the mean is that of shrinkage towards the origin. This result is generalized to skew-elliptical distributions.

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  • Umbach, Dale, 2008. "Some moment relationships for multivariate skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1619-1623, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1619-1623
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    References listed on IDEAS

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    1. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "Moments of random vectors with skew t distribution and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 417-423, July.
    2. Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.
    3. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
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    Cited by:

    1. Adelchi Azzalini & Giuliana Regoli, 2012. "Some properties of skew-symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 857-879, August.

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