小瓢虫传媒

An introduction to symmetry-modulated distributions

Adelchi Azzalini, University of Padua

The term "symmetry-modulated distributions" refers to a general procedure for generating distributions starting from an baseline symmetric density function and modulating it according to a simple rule which ensures that this process always delivers a proper probability distribution. The archetypal representative of this formulation is represented by the skew-normal distribution, but the underlying procedure applies much more generally. In fact, the method applies both to the univariate and to the multivariate context, in a parametric or a semi-parametric formulation; it is targeted primarily to the context of continuous variables, although the discrete case is also possible. We shall review the main ingredients and properties of this formulation and sketch briefly some connections with themes in econometrics and finance.