A class of skew-multivariate distributions for spatial data

TL;DR

This paper develops a new class of copula-based multivariate Pareto-mixture models for spatial data, capable of capturing complex tail dependence, asymmetry, and providing practical tools for analysis.

Contribution

It introduces a flexible, tractable class of skew-multivariate distributions for spatial data, with demonstrated effectiveness in modeling tail behaviors and real-world temperature data.

Findings

Models effectively capture tail dependence and asymmetry.

Simulation studies show good finite-sample performance.

Application to temperature data demonstrates practical utility.

Abstract

This paper introduces a class of copula models for spatial data, based on multivariate Pareto-mixture distributions. We explore the tail properties of these models, demonstrating their ability to capture both tail dependence and asymptotic independence, as well as the tail asymmetry frequently observed in real-world data. The proposed models also offer flexibility in accounting for permutation asymmetry and can effectively represent both the bulk and extreme tails of the distribution. We consider special cases of these models with computationally tractable likelihoods and present an extensive simulation study to assess the finite-sample performance of the maximum likelihood estimators. Finally, we apply our models to analyze a temperature dataset, showcasing their practical utility.