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Marginal replacement in multivariate densities, with application to skewing spherically symmetric distributions. (English) Zbl 0998.60016
Summary: We consider a simple general construct, that of marginal replacement in a multivariate distribution, that provides, in particular, an interesting way of producing distributions that have a skew marginal from spherically symmetric starting points. Particular examples include a new multivariate beta distribution and a new multivariate \(t/\text{skew} t\) distribution, along with Azzalini and colleagues’ multivariate skew normal distribution.

MSC:
60E05 Probability distributions: general theory
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