Skewed multivariate models related to hidden truncation and/or selective reporting

The univariate skew-normal distribution was introduced by Azzalini in 1985 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. Arnold et al. (1993) introduced a more general skew-normal distribution as the marginal distribution of a truncated bivariate normal distribution in whichX was retained only ifY 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.