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

2024/08/30 by Roberto Vila, Vila, Roberto, Helton Saulo +7
Environmental Science · Mathematics · #60E05 #62Exx #62Fxx #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Hydrology and Drought Analysis #Methodology (stat.ME) #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2408.17410

openalex publication_date 2024/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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