A skew-symmetric representation of multivariate distributions

Statistica Sinica

Volumn 14, Issue 4, 2004, Pages 1259-1270

  Wang, Jiuzhou ^a   Boyer, Joseph ^a   Genton, Marc G ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Elliptical; Kurtosis; Multimodality; Quadratic form; Skewness; Stochastic representation

Indexed keywords

EID: 4043103972     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Arellano-Valle, R. B., del Pino, G. and San Martin, E. (2002). Definition and probabilistic properties of skew-distributions. Statist. Probab. Lett. 58, 111-121.
2. Arnold, B. C. and Beaver, R. J. (2000). The skew-Cauchy distribution. Statist. Probab. Lett. 49, 285-290.
3. Arnold, B. C. and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test 11, 7-54.
4. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.
5. Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones, Statistica 46, 199-208.
6. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715-726.
7. Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution. J. Roy. Statist. Soc. Ser. B 61, 579-602.
8. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367-389.
9. Branco, M. D. and Dey, D. K. (2001). A general class of multivariate skew-elliptical distributions. J. Multivariate Anal. 79, 99-113.
10. Domínguez-Molina, J. A., González-Farías, G. and Gupta, A. K. (2001). A general multivariate skew-normal distribution. Technical Report No. 01-09. Department of Mathematics and Statistics, Bowling Green State University.
11. Genton, M. G., He, L. and Liu, X. (2001). Moments of skew-normal random vectors and their quadratic forms. Statist. Probab. Lett. 51, 319-325.
12. Genton, M. G. and Loperfido, N. (2002). Generalized skew-elliptical distributions and their quadratic forms. Institute, of Statistics Mirneo Series #2539, to appear in Ann. Inst. Statist. Math.
13. Loperfido, N. (2001). Quadratic forms of skew-normal random vectors. Statist. Probab. Lett. 54, 381-387.
14. Sahu, S. K., Dey, D. K. and Branco, M. D. (2003). A new class of multivariate skew distributions with applications to Bayesian regression models. Canad. J. Statist. 31, 129-150.
15. Wahed, A. and Ali, M. M. (2001). The skew-logistic distribution. J. Statist. Res. 35, 71-80.
16. Wang, J., Boyer, J. and Genton, M. G. (2004). A note on an equivalence between chi-square and generalized skew-normal distributions. Statist. Probab. Lett. 66, 395-398.