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On The Canonical Form Of Scale Mixtures Of Skew-Normal Distributions

Author

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  • Antonella Capitanio

    (Università di Bologna)

Abstract

The canonical form of scale mixtures of multivariate skew-normal distribution is defined, emphasizing its role in summarizing some key properties of this class of distributions. It is also shown that the canonical form corresponds to an affine invariant co-ordinate system as defined in Tyler et al. (2009), and a method for obtaining the linear transform that converts a scale mixture of multivariate skew-normal distribution into a canonical form is presented. Related results, where the particular case of the multivariate skew t distribution is considered in greater detail, are the general expression of the Mardia indices of multivariate skewness and kurtosis and the reduction of dimensionality in calculating the mode.

Suggested Citation

  • Antonella Capitanio, 2020. "On The Canonical Form Of Scale Mixtures Of Skew-Normal Distributions," Statistica, Department of Statistics, University of Bologna, vol. 80(2), pages 145-160.
    • Handle: RePEc:bot:rivsta:v:80:y:2020:i:2:p:145-160
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    Cited by:

    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Baishuai Zuo & Narayanaswamy Balakrishnan & Chuancun Yin, 2023. "An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions," Papers 2311.18176, arXiv.org.
    3. Christopher J. Adcock, 2022. "Properties and Limiting Forms of the Multivariate Extended Skew-Normal and Skew-Student Distributions," Stats, MDPI, vol. 5(1), pages 1-42, March.

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