Jones, M. C.
Marginal replacement in multivariate densities, with application to skewing spherically symmetric distributions.
Journal of Multivariate Analysis, 81(1) pp. 85–99.
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/skew t distribution, along with Azzalini and colleagues' multivariate skew normal distribution.
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