ON THE CANONICAL FORM OF SCALE MIXTURES OF SKEW-NORMAL DISTRIBUTIONS

Antonella Capitanio ()
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Antonella Capitanio: Università di Bologna

Statistica, 2020, vol. 80, issue 2, 145-160

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.

Keywords: Affine invariance; Kurtosis; Mardia indices of multivariate skewness and kurtosis; Scale mixtures of normal distributions; Skewness; Skew-normal distribution; Skew t distribution (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:bot:rivsta:v:80:y:2020:i:2:p:145-160

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