# zbMATH — the first resource for mathematics

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:
 6e+06 Probability distributions: general theory
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.