Selection models under generalized symmetry settings
- First Online:
- 122 Downloads
An active stream of literature has followed up the idea of skew-elliptical densities initiated by Azzalini and Capitanio (J. R. Stat. Soc. Ser. B 61:579–602, 1999). Their original formulation was based on a general lemma which is however of broader applicability than usually perceived. This note examines new directions of its use, and illustrates them with the construction of some probability distributions falling outside the family of the so-called skew-symmetric densities.
KeywordsCentral symmetry Gamma distribution Probability integral transform Skew-normal distribution Skew-symmetric distributions Symmetric functions Symmetry
Unable to display preview. Download preview PDF.
- Azzalini, A., Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution. Journal of the Royal Statistical Society, series B, 61, 579–602. Full version of the paper at arXiv.org:0911.2093.Google Scholar
- Azzalini, A., Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society, series B, 65, 367–389. Full version of the paper at arXiv.org:0911.2342.Google Scholar
- Genton, M. G., Ed. (2004). Skew-elliptical Distributions and Their Applications: a Journey Beyond Normality. Boca Raton: Chapman & Hall/CRC.Google Scholar
- Serfling R. (2006) Multivariate symmetry and asymmetry. In: Kotz S., Balakrishnan N., Read C.B., Vidakovic B. (eds) Encyclopedia of Statistical Sciences (2nd ed, Vol. 8). J. Wiley & Sons, New York, pp 5338–5345Google Scholar