The Multivariate Alpha Skew Gaussian Distribution
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In this paper we propose a new class of probability distributions, so called multivariate alpha skew normal distribution. It can accommodate up to two modes and generalizes the distribution proposed by Elal-Olivero [Proyecciones (Antofagasta) 29(3):224–240, 2010] in its marginal components. Its properties are studied. In particular, we derive its standard and non-standard densities, moment generating functions, expectations, variance-covariance matrixes, marginal and conditional distributions. Estimation is based on maximum likelihood. The asymptotic properties of the inferential procedure are verified in the light of a simulation study. The usefulness of the new distribution is illustrated in a real benchmark data.
KeywordsAlpha skew Gaussian distribution Asymmetry Bimodality Multivariate distribution
The authors thank the reviewers for their comments and suggestions, which led to a substantial improvement of the manuscript. The research was partial sponsored by the Brazilian organizations CNPq ans FAPESP through their research grant programs.
- Bahrami, W., Agahi, H., Rangin, H.: A two-parameter balakrishnan skew-normal distribution. J. Stat. Res. Iran 6, 231–242 (2009)Google Scholar
- Everitt, B.S., Hothorn, T.: Maintainer Torsten Hothorn, and Chapman Everitt. Package HSAUR3 (2014)Google Scholar
- Kotecha, J.H., Djuric, P.M.: Gibbs sampling approach for generation of truncated multivariate gaussian random variables. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, 1999, Proceedings, vol. 3, pp. 1757–1760 (1999)Google Scholar
- Louzada, F., Ara, A., Fernandes, G.: The bivariate alpha-skew-normal distribution. Commun. Stat.-Theory Methods (2016) (just-accepted) Google Scholar
- Mahalanobis, P.C.: On the Generalized Distance in Statistics. In: Proceedings of National Institute of Sciences (India), vol. 2, pp. 49–55 (1936)Google Scholar
- R Core Team: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2013)Google Scholar
- Seber, G.A.F.: Linear Regression Analysis. Wiley, New York (1977)Google Scholar