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Skewed multivariate models related to hidden truncation and/or selective reporting. With discussion and a rejoinder by the authors. (English) Zbl 1033.62013
Summary: The univariate skew-normal distribution was introduced by A. Azzalini [Scand. J. Stat., Theory Appl. 12, 171–178 (1985; Zbl 0581.62014)] as a natural extension of the classical normal density to accommodate asymmetry. He extensively studied the properties of this distribution and, in conjunction with coauthors, extended this class to include the multivariate analog of the skew-normal. B. C. Arnold et al. [Psychometrika 58, 471–488 (1993; Zbl 0794.62075)] introduced a more general skew-normal distribution as the marginal distribution of a truncated bivariate normal distribution in which \(X\) was retained only if \(Y\) satisfied certain constraints. Using this approach, more general univariate and multivariate skewed distributions have been developed. A survey of such models is provided together with discussion of related inference questions.

MSC:
62E10 Characterization and structure theory of statistical distributions
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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