Generalized skew-elliptical distributions and their quadratic forms.

*(English)*Zbl 1083.62043Summary: This paper introduces generalized skew-elliptical distributions (GSE), which include the multivariate skew-normal, skew-\(t\), skew-Cauchy, and skew-elliptical distributions as special cases. GSE are weighted elliptical distributions but the distribution of any even function in GSE random vectors does not depend on the weight function. In particular, this holds for quadratic forms in GSE random vectors. This property is beneficial for inference from non-random samples. We illustrate the latter point on a data set of Australian athletes.

##### MSC:

62H05 | Characterization and structure theory for multivariate probability distributions; copulas |

62H12 | Estimation in multivariate analysis |

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\textit{M. G. Genton} and \textit{N. M. R. Loperfido}, Ann. Inst. Stat. Math. 57, No. 2, 369--401 (2005; Zbl 1083.62043)

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