A family of multivariate extended skew-G-elliptical distributions

The supplementary material provides the complete R script used to generate pseudo-random samples and compute the maximum-likelihood estimates. In this paper, we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties, including the characterization of the density function for various distribution types, as well as other key aspects such as quantiles, stochastic representation, conditional and marginal distributions, moments and parameter estimation. A Monte Carlo simulation study is performed for examining the performance of the developed parameter estimation method. Finally, the proposed models are used to analyze socioeconomic data.