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Distribution of quadratic forms under skew normal settings

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  • Wang, Tonghui
  • Li, Baokun
  • Gupta, Arjun K.

Abstract

For a class of multivariate skew normal distributions, the noncentral skew chi-square distribution is studied. The necessary and sufficient conditions under which a sequence of quadratic forms is generalized noncentral skew chi-square distributed random variables are obtained. Several examples are given to illustrate the results.

Suggested Citation

  • Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:533-545
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    References listed on IDEAS

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    1. Arjun Gupta & John Chen, 2004. "A class of multivariate skew-normal models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 305-315, June.
    2. Fang, B. Q., 2003. "The skew elliptical distributions and their quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 298-314, November.
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    5. 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.
    6. 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.
    7. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
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    Cited by:

    1. Rendao Ye & Tonghui Wang & Saowanit Sukparungsee & Arjun Gupta, 2015. "Tests in variance components models under skew-normal settings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 885-904, October.
    2. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    3. Li, Baokun & Tian, Weizhong & Wang, Tonghui, 2018. "Remarks for the singular multivariate skew-normal distribution and its quadratic forms," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 105-112.
    4. Young, Phil D. & Harvill, Jane L. & Young, Dean M., 2016. "A derivation of the multivariate singular skew-normal density function," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 40-45.
    5. Zheng Wei & Seongyong Kim & Boseung Choi & Daeyoung Kim, 2019. "Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 365-387, January.
    6. Young, Phil D. & Kahle, David J. & Young, Dean M., 2017. "On the independence of singular multivariate skew-normal sub-vectors," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 58-62.
    7. Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
    8. Robert Paige & A. Trindade & R. Wickramasinghe, 2014. "Extensions of saddlepoint-based bootstrap inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 961-981, October.
    9. Marchand, Éric & Strawderman, William E., 2020. "On the non-stochastic ordering of some quadratic forms," Statistics & Probability Letters, Elsevier, vol. 163(C).
    10. Olcay Arslan, 2015. "Variance-mean mixture of the multivariate skew normal distribution," Statistical Papers, Springer, vol. 56(2), pages 353-378, May.

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