Family of multivariate extended skew-elliptical distributions: Statistical properties, inference and application

TL;DR

This paper introduces a new family of multivariate asymmetric distributions based on elliptically symmetric distributions, exploring their properties, estimation methods, and applications to socioeconomic data.

Contribution

It defines a flexible family of multivariate extended skew-elliptical distributions and investigates their statistical properties, inference procedures, and practical application.

Findings

Distribution properties characterized including density, moments, and stochastic representation.

Parameter estimation method evaluated via Monte Carlo simulations.

Models successfully applied to socioeconomic data analysis.

Abstract

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 identifiability, quantiles, stochastic representation, conditional and marginal distributions, moments, Kullback-Leibler Divergence, 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.