×

A multivariate skew normal distribution. (English) Zbl 1036.62043

Summary: We define a new class of multivariate skew-normal distributions. Its properties are studied. In particular, we derive its density, moment generating function, the first two moments and marginal and conditional distributions. We illustrate the contours of a bivariate density as well as conditional expectations. We also give an extension to construct a general multivariate skew normal distribution.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] R. Arellano-Valle, G. Del Pino, E. San Martin, A general class of skew-distributions, Publicaciones técnicas, Centro de modelamiento matemático, Universidad de Chile UMR-CNRS, 2001.
[2] Arnold, B.C.; Beaver, R.J., Skew multivariate models related to hidden truncation and/or selective reporting, Test. sociedad de estadı́stica e investigación operativa., 11, 1, 7-54, (2002) · Zbl 1033.62013
[3] Azzalini, A., A class of distributions which includes the normal ones, Scand. J. statist., 12, 171-178, (1985) · Zbl 0581.62014
[4] Azzalini, A., Further results on a class of distributions which includes the normal ones, Statistica, 46, 199-208, (1986) · Zbl 0606.62013
[5] Azzalini, A.; Capitanio, A., Statistical applications of the multivariate skew normal distribution, J. roy. statist. soc. B, 61, 579-602, (1999) · Zbl 0924.62050
[6] Azzalini, A.; Dalla-Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 715-726, (1996) · Zbl 0885.62062
[7] Bjerve, S.; Doksum, K., Correlation curvesmeasures of association as function of covariate values, Ann. statist., 21, 2, 890-902, (1993) · Zbl 0817.62025
[8] J.A. Domı́nguez-Molina, G. González-Farı́as, A.K. Gupta, A General Multivariate Skew Normal Distribution, Department of Mathematics and Statistics, Bowling Green State University, Technical Report No. 01-09, 2001.
[9] Genton, M.G.; He, L.; Liu, X., Moments of skew-normal random vectors and their quadratic forms, Statist. probab. lett., 51, 319-325, (2001) · Zbl 0972.62031
[10] A.K. Gupta, G. Gonzáles-Farı́as, Domı́nguez-Molina, A Multivariate Skew Normal Distribution, Department of Mathematics and Statistics, Bowling Green State University, Technical Report No. 01-10, 2001.
[11] Marsaglia, G., Expressing the normal distribution with covariance matrix A+B in terms of one with covariance matrix A, Biometrika, 50, 535-538, (1963) · Zbl 0117.37202
[12] S. Zacks, Parametric Statistical Inference, Oxford, Pergamon, 1981. · Zbl 0452.62020
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.