Graphical models for skew-normal variates. (English) Zbl 1035.60008
A skew-normal distribution is an \(R^k\) distribution with PDF \(\varphi(y-\xi;\Omega)\Phi(\alpha_0+\alpha^T\omega^{-1}(y-\xi))/\Phi(\tau)\), where \(\varphi(y;\Omega)\) is the density of \(N(0,\Omega)\), \(\Phi\) is \(N(0,1)\) CDF, \(\omega=\text{diag}(\Omega_{11},\dots,\Omega_{kk})^{1/2}\), \(\alpha\) and \(\tau\) are parameters, \(\alpha_0\) is a function of \((\Omega,\alpha,\tau)\). Properties of such distributions are described; marginal and conditional distributions, conditions of independence are discussed. The construction of dependence graphs is described. A maximum likelihood estimate is proposed for the parameters.
Reviewer: R. E. Maiboroda (Kyïv)
MSC:
| 60E05 | Probability distributions: general theory |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Keywords:
conditional independence graph; parameter based factorization; marginal distribution; independenceReferences:
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