Flexible class of skew-symmetric distributions. (English) Zbl 1063.62079
A class of flexible skew-symmetric (FSS) distributions on \(\mathbb R^p\) consists of distributions with PDF of the form \(2f(x-\xi)H(P_k(x-\xi))\), where \(f\) is a symmetric PDF, \(H:{\mathbb R}\to[0,1]\) is a continuous CDF symmetric around zero, \(P_k\) is a polynomial on \({\mathbb R}^p\) of degree \(k\). It is shown that FSS is a dense subclass of the class of skew-symmetric distributions in \(L_{\infty}\) norm. Statistical fitting of such distributions to real data is discussed.
Reviewer: R. E. Maiboroda (Kyïv)
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62H10 | Multivariate distribution of statistics |
| 60E05 | Probability distributions: general theory |
| 62F12 | Asymptotic properties of parametric estimators |
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