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Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution

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  • Mehdi Amiri
  • Ahad Jamalizadeh
  • Mina Towhidi

Abstract

In this paper the normal-skew-normal distribution, proposed by Gomez et al. (Statistics 47:411–421, 2013 ), is extended to the multivariate case. It is also a special case of $$SUN_{n,2}$$ S U N n , 2 -distribution, recently studied by Arellano-Valle and Genton (Chil J Stat 2:17–34, 2010 ). We show that the proposed distribution can be expressed as a shape mixture of the multivariate extended skew-normal distribution. Applying this property leads to deriving stochastic representations for the proposed distribution. Also we give some basic properties for this new family. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates. Finally, an application of the new distribution is illustrated using some real data sets. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Mehdi Amiri & Ahad Jamalizadeh & Mina Towhidi, 2015. "Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution," Statistical Papers, Springer, vol. 56(4), pages 1071-1098, November.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1071-1098
    DOI: 10.1007/s00362-014-0625-3
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