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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.

60E05 Probability distributions: general theory
Full Text: DOI
[1] Azzalini, A., A class of distributions which includes the normal ones, Scand. J. statist., 12, 171-178, (1985) · Zbl 0581.62014
[2] Azzalini, A.; Capitanio, A., Statistical applications of the multivariate skew-normal distribution, J. roy. statist. soc. ser. B, 61, 579-602, (1999) · Zbl 0924.62050
[3] Azzalini, A.; Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 715-726, (1996) · Zbl 0885.62062
[4] Fang, K.T.; Kotz, S.; Ng, K.W., Symmetric multivariate and related distributions, (1990), Chapman and Hall London
[5] Holland, P.W.; Wang, Y.J., Dependence function for continuous bivariate densities, Commun. statist. theory methods, 16, 863-876, (1987) · Zbl 0609.62092
[6] Joe, H., Multivariate models and dependence concepts, (1997), Chapman and Hall London · Zbl 0990.62517
[7] Johnson, N.L.; Kotz, S., Distributions in statistics: continuous multivariate distributions, (1972), Wiley New York · Zbl 0248.62021
[8] Jones, M.C., The local dependence function, Biometrika, 83, 899-904, (1996) · Zbl 0883.62057
[9] Jones, M.C., A skew t distribution, (), 269-278
[10] M. C. Jones, and, M. J. Faddy, A skew extension of the t distribution with applications, manuscript submitted for publication. · Zbl 1063.62013
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