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Generalized skew-elliptical distributions are closed under affine transformations

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  • Shushi, Tomer

Abstract

In this short letter we prove that the family of multivariate generalized skew-elliptical distributions is closed under affine transformations. This fundamental property has many applications in applied and theoretical probability.

Suggested Citation

  • Shushi, Tomer, 2018. "Generalized skew-elliptical distributions are closed under affine transformations," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 1-4.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:1-4
    DOI: 10.1016/j.spl.2017.10.012
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    References listed on IDEAS

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    1. Nicola Loperfido, 2010. "Canonical transformations of skew-normal variates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 146-165, May.
    2. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
    3. Shushi, Tomer, 2016. "A proof for the conjecture of characteristic function of the generalized skew-elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 301-304.
    4. Balakrishnan, N. & Scarpa, Bruno, 2012. "Multivariate measures of skewness for the skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 73-87, February.
    5. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
    6. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
    7. Arevalillo, Jorge M. & Navarro, Hilario, 2015. "A note on the direction maximizing skewness in multivariate skew-t vectors," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 328-332.
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    Cited by:

    1. Shushi, Tomer, 2018. "A proof for the existence of multivariate singular generalized skew-elliptical density functions," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 50-55.
    2. Shushi, Tomer, 2019. "A note on the coefficients of elliptical random variables," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 153-155.
    3. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    4. Eini, Esmat Jamshidi & Khaloozadeh, Hamid, 2021. "The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 44-50.

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