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A suite of commands for fitting the skew-normal and skew-t models

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  • Yulia V. Marchenko

    (StataCorp)

  • Marc G. Genton

    (Texas A&M University)

Abstract

Nonnormal data arise often in practice, prompting the development of flexible distributions for modeling such situations. In this article, we describe two multivariate distributions, the skew-normal and the skew-t, which can be used to model skewed and heavy-tailed continuous data. We then discuss some inferential issues that can arise when fitting these distributions to real data. We also consider the use of these distributions in a regression setting for more flexible parametric modeling of the conditional distribution given other predictors. We present commands for fitting univariate and multivariate skew-normal and skew-t regressions in Stata (skewnreg, skewtreg, mskewnreg, and mskewtreg) as well as some postestimation features (predict and skewrplot). We also demonstrate the use of the commands for the analysis of the famous Australian Institute of Sport data and U.S. precipitation data. Copyright 2010 by StataCorp LP.

Suggested Citation

  • Yulia V. Marchenko & Marc G. Genton, 2010. "A suite of commands for fitting the skew-normal and skew-t models," Stata Journal, StataCorp LP, vol. 10(4), pages 507-539, December.
    • Handle: RePEc:tsj:stataj:v:10:y:2010:i:4:p:507-539
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    References listed on IDEAS

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    1. 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.
    2. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
    3. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    4. 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.
    5. Roberto G. Gutierrez & Shana Carter & David M. Drukker, 2001. "On boundary-value likelihood-ratio tests," Stata Technical Bulletin, StataCorp LP, vol. 10(60).
    6. Nicholas J. Cox, 2010. "Speaking Stata: The statsby strategy," Stata Journal, StataCorp LP, vol. 10(1), pages 143-151, March.
    7. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    8. 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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    Cited by:

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    3. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
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    7. Mussida, Chiara & Parisi, Maria Laura, 2017. "Ethnic groups' income inequality within and across Italian regions," MPRA Paper 85788, University Library of Munich, Germany.
    8. Wenxia Ge & Jeong-Bon Kim, 2014. "Boards, takeover protection, and real earnings management," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 651-682, November.

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