Flexible asymmetric multivariate distributions based on two-piece univariate distributions

Jonas Baillien, Irène Gijbels () and Anneleen Verhasselt
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Jonas Baillien: KU Leuven
Irène Gijbels: KU Leuven
Anneleen Verhasselt: Hasselt University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 1, No 7, 159-200

Abstract: Abstract Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple distributions, grouped under the name “skewed distributions”, have been developed to specifically cope with asymmetric data. In this paper, we present a broad family of flexible multivariate skewed distributions for which statistical inference is a feasible task. The studied family of multivariate skewed distributions is derived by taking affine combinations of independent univariate distributions. These are members of a flexible family of univariate asymmetric distributions and are an important basis for achieving statistical inference. Besides basic properties of the proposed distributions, also statistical inference based on a maximum likelihood approach is presented. We show that under mild conditions, weak consistency and asymptotic normality of the maximum likelihood estimators hold. These results are supported by a simulation study confirming the developed theoretical results, and some data examples to illustrate practical applicability.

Keywords: Affine combination; Maximum likelihood estimation; Multivariate skew distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00842-6

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