Advanced SearchSearch Tips
On Perturbed Symmetric Distributions Associated with the Truncated Bivariate Elliptical Models
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
On Perturbed Symmetric Distributions Associated with the Truncated Bivariate Elliptical Models
Kim, Hea-Jung;
  PDF(new window)
This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.
Perturbed symmetric distribution;truncated bivariate elliptical distribution;Skew-elliptical distribution;
 Cited by
Arellano-Valle, R. B., Branco, M. D. and Genton, M. G. (2006). A unified view on skewed distributions arising from selections, The Canadian Journal of Statistics/La revue Canadienne de Ststistique, 34, 581-601 crossref(new window)

Arnold, B. C., Beaver, R. J., Groeneveld, R. A. and Meeker, W. Q. (1993). The non-truncated marginal of a truncated bivariate normal distribution, Psychometrika, 58, 471-488 crossref(new window)

Azzalini, A. (1985). A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution, Journal of the Royal Statistical Society, Ser.B, 35, 367-389

Branco, M. D. and Dey, D. K. (2001). A general class of multivariate skew elliptical distributions, Journal of Multivariate Analysis, 79, 99-113 crossref(new window)

Chen, M. H. and Dey, D. K. (1998). Bayesian modeling of correlated binary responses via scale mixture of multivariate normal link functions, Sankhya, 60, 322-343

Devroye, L. (1986). Non-Uniform Random Variate Generation, Springer Verlag, New York

Fang, K. T., Kotz, S. and Ng, K. W. (1990). Symmetric Multivariate and Related Distributions, Chapman & Hall/CRC, New York

Fang, K. T. and Zhang, Y. T. (1990). Generalized Multivariate Analysis, Springer-Verlag, New York

Henze, N. (1986). A probabilistic representation of the 'Skew-normal' distribution, Scandinavian Journal of Statistics, 13, 271-275

Johnson, N. L. and Kotz, S. (1972). Distributions in Statistics: Continuous Multivariate Distributions, John Wiley & Sons, New York

Kim, H. J. (2002). Binary regression with a class of skewed t link models, Communications in Statistics-Theory and Methods, 31, 1863-1886 crossref(new window)

Kim, H. J. (2007). A class of weighted normal distributions and its variants useful for inequality constrained analysis, Statistics, 41, 421-441 crossref(new window)

Kim, H. J. (2008). A class of weighted multivariate normal distributions and its properties, Journal of the Multivariate Analysis, In press, doi:10.1016/j.jmva.2008.01.008

Ma, Y. and Genton, M. G. (2004). A flexible class of skew-symmetric distributions, Scandinavian Journal of Statistics, 31, 459-468 crossref(new window)

Rudy, D. A. (2002). Intermediate Microeconomic Theory, Digital Authoring Resources, Denver