Algorithm 462: bivariate normal distribution
Communications of the ACM
A general class of multivariate skew-elliptical distributions
Journal of Multivariate Analysis
Classification of a screened data into one of two normal populations perturbed by a screening scheme
Journal of Multivariate Analysis
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This article proposes a class of weighted multivariate normal distributions whose probability density function has the form of a product of a multivariate normal density and a weighting function. The class is obtained from marginal distributions of various doubly truncated multivariate normal distributions. The class strictly includes the multivariate normal and multivariate skew-normal. It is useful for selection modeling and inequality constrained normal mean vector analysis. We report on a study of some distributional properties and the Bayesian perspective of the class. A probabilistic representation of the distributions is also given. The representation is shown to be straightforward to specify the distribution and to implement computation, with output readily adapted for the required analysis. Necessary theories and illustrative examples are provided.