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Quadratic forms of skew-normal random vectors

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  • Loperfido, Nicola

Abstract

The sum of squares and products matrix has a Wishart distribution, when the rows of the corresponding data matrix are i.i.d. according to a skew-normal distribution centered at the origin. Applications include robustness of the t-test, time series and spatial statistics.

Suggested Citation

  • Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:381-387
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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. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    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. Behboodian, J. & Jamalizadeh, A. & Balakrishnan, N., 2006. "A new class of skew-Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1488-1493, August.
    2. A. Jamalizadeh & A. Arabpour & N. Balakrishnan, 2011. "A generalized skew two-piece skew-normal distribution," Statistical Papers, Springer, vol. 52(2), pages 431-446, May.
    3. Kahrari, F. & Rezaei, M. & Yousefzadeh, F. & Arellano-Valle, R.B., 2016. "On the multivariate skew-normal-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 80-88.
    4. Samuel Kotz & Donatella Vicari, 2005. "Survey of developments in the theory of continuous skewed distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 225-261.
    5. Fang, B.Q., 2008. "Noncentral matrix quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1105-1127, July.
    6. 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.
    7. Fang, B.Q., 2005. "Noncentral quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 410-430, August.
    8. Huang, Wen-Jang & Chen, Yan-Hau, 2006. "Quadratic forms of multivariate skew normal-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 871-879, May.
    9. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    10. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.

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