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Some moment relationships for skew-symmetric distributions

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  • Umbach, Dale

Abstract

For univariate skew-symmetric distributions in a general setting, odd moments are increasing functions of the skewing parameter and even moments do not depend on this parameter. Skewness, however, has no such order relations. The relationship between skew and the skewing parameter can be complicated.

Suggested Citation

  • Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:5:p:507-512
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    References listed on IDEAS

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    1. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
    2. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
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    Cited by:

    1. V. Nekoukhou & M. Alamatsaz, 2012. "A family of skew-symmetric-Laplace distributions," Statistical Papers, Springer, vol. 53(3), pages 685-696, August.
    2. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    3. Umbach, Dale, 2008. "Some moment relationships for multivariate skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1619-1623, September.
    4. Dale Umbach & Sreenivas Rao Jammalamadaka, 2010. "Some moment properties of skew-symmetric circular distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 265-273.
    5. Mahdi Salehi & Adelchi Azzalini, 2018. "On application of the univariate Kotz distribution and some of its extensions," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 177-201, August.
    6. 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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    Keywords

    Skew-symmetric Skewness Moments;

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