The Skew-normal Distribution and Related Multivariate Families*


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    This paper was presented at the 20th Nordic Conference on Mathematical Statistics, Jyväskylä, June 2004 (NORDSTAT 2004).

Adelchi Azzalini, Dipartimento di Scienze Statistiche, Università di Padova, Italy.


Abstract.  This paper provides an introductory overview of a portion of distribution theory which is currently under intense development. The starting point of this topic has been the so-called skew-normal distribution, but the connected area is becoming increasingly broad, and its branches include now many extensions, such as the skew-elliptical families, and some forms of semi-parametric formulations, extending the relevance of the field much beyond the original theme of ‘skewness’. The final part of the paper illustrates connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non-linear time series, especially in connection with financial data, and more.