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The Multivariate Alpha Skew Gaussian Distribution

  • Anderson AraEmail author
  • Francisco Louzada
Article
  • 34 Downloads

Abstract

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.

Keywords

Alpha skew Gaussian distribution Asymmetry Bimodality Multivariate distribution 

Notes

Acknowledgements

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.

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Copyright information

© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Departamento de EstatísticaUniversidade Federal da BahiaSalvadorBrazil
  2. 2.Instituto de Matemática e Ciências da ComputaçãoUniversidade de São PauloSão CarlosBrazil

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