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An Alternative Matrix Skew-Normal Random Matrix and Some Properties

Author

Listed:
  • Phil D. Young

    (Baylor University)

  • Joshua D. Patrick

    (Baylor University)

  • John A. Ramey

    (Novi Labs)

  • Dean M. Young

    (Baylor University)

Abstract

We propose an alternative skew-normal random matrix, which is an extension of the multivariate skew-normal vector parameterized in Vernic (A Stiint Univ Ovidius Constanta. 13, 83–96 2005, Insur. Math. Econ.38, 413–426 2006). We define the density function and then derive and apply the corresponding moment generating function to determine the mean matrix, covariance matrix, and third and fourth moments of the new skew-normal random matrix. Additionally, we derive eight marginal and two conditional density functions and provide necessary and sufficient conditions such that two pairs of sub-matrices are independent. Finally, we derive the moment generating function for a skew-normal random matrix-based quadratic form and show its relationship to the moment generating function of the noncentral Wishart and central Wishart random matrices.

Suggested Citation

  • Phil D. Young & Joshua D. Patrick & John A. Ramey & Dean M. Young, 2020. "An Alternative Matrix Skew-Normal Random Matrix and Some Properties," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 28-49, February.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:1:d:10.1007_s13171-019-00165-4
    DOI: 10.1007/s13171-019-00165-4
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    References listed on IDEAS

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    1. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, 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.
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    5. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
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    7. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.
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