The Multivariate Skew Normal Distribution and Some Extensions

Antonella Capitanio

The multivariate skew normal distribution extends the class of normal distributions by the addition of a shape parameter. It allows to model phenomena whose empirical outcome behaves in non-normal fashion but still retains some similarity with the normal distribution. It has been introduced in Azzalini & Dalla Valle (1996), and further probabilistic properties as well as statistical aspects have been explored in Azzalini and Capitanio (1999). As a natural extension, Azzalini and Capitanio (2003) considered the class of distributions generated by perturbation of central symmetry, and studied in detail the particular case of skew elliptical distributions. In this talk the main properties of these families will be illustrated.


Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution. J. R. Statist. Soc. B, 61, 579-602. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J. R. Statist. Soc. B, 65, 367-389. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew normal distribution. Biometrika.

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