2012/07/03 by Antonella Capitanio, Capitanio, Antonella
Decision Sciences · Mathematics · #62E99 #62H99 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #msc:62E99 #msc:62H99 #stat.ME
paper · pdf · doi:10.48550/arxiv.1207.0797
14 pages
arxiv created 2012/07/03 · openalex publication_date 2012/07/03 · arxiv updated 2012/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.