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Three skewed matrix variate distributions

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  • Gallaugher, Michael P.B.
  • McNicholas, Paul D.

Abstract

Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix variate distributions that incorporate skewness, as well as other flexible properties such as concentration, are discussed. Equivalences to multivariate analogues are presented, and moment generating functions are derived. Maximum likelihood parameter estimation is discussed, and simulated data is used for illustration.

Suggested Citation

  • Gallaugher, Michael P.B. & McNicholas, Paul D., 2019. "Three skewed matrix variate distributions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 103-109.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:103-109
    DOI: 10.1016/j.spl.2018.08.012
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    References listed on IDEAS

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    1. O’Hagan, Adrian & Murphy, Thomas Brendan & Gormley, Isobel Claire & McNicholas, Paul D. & Karlis, Dimitris, 2016. "Clustering with the multivariate normal inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 18-30.
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    Cited by:

    1. Michael P. B. Gallaugher & Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2022. "Multivariate cluster weighted models using skewed distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 93-124, March.
    2. Michael P. B. Gallaugher & Paul D. McNicholas, 2020. "Mixtures of skewed matrix variate bilinear factor analyzers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 415-434, June.
    3. Rezaei, Amir & Yousefzadeh, Fatemeh & Arellano-Valle, Reinaldo B., 2020. "Scale and shape mixtures of matrix variate extended skew normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    4. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    5. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    6. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.

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    Keywords

    Matrix variate; Skewed distributions;

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