1. Flexible asymmetric multivariate distributions based on two-piece univariate distributions.
- Author
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Baillien, Jonas, Gijbels, Irène, and Verhasselt, Anneleen
- Subjects
- *
DISTRIBUTION (Probability theory) , *SKEWNESS (Probability theory) , *ASYMPTOTIC normality , *MAXIMUM likelihood statistics , *GAUSSIAN distribution - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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