A multivariate modified skew-normal distribution

Sagnik Mondal (), Reinaldo B. Arellano-Valle () and Marc G. Genton ()
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Sagnik Mondal: King Abdullah University of Science and Technology
Reinaldo B. Arellano-Valle: Pontificia Universidad Católica de Chile
Marc G. Genton: King Abdullah University of Science and Technology

Statistical Papers, 2024, vol. 65, issue 2, No 2, 555 pages

Abstract: Abstract We introduce a multivariate version of the modified skew-normal distribution, which contains the multivariate normal distribution as a special case. Unlike the Azzalini multivariate skew-normal distribution, this new distribution has a nonsingular Fisher information matrix when the skewness parameters are all zero, and its profile log-likelihood of the skewness parameters is always a non-monotonic function. We study some basic properties of the proposed family of distributions and present an expectation-maximization (EM) algorithm for parameter estimation that we validate through simulation studies. Finally, we apply the proposed model to the univariate frontier data and to a trivariate wind speed data, and compare its performance with the Azzalini skew-normal model.

Keywords: EM algorithm; Fisher information matrix; Modified skew-normal; Skew-elliptical; Skew-generalized normal; Skew-normal (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01397-1

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