# Exploring the Distributional Properties of the Non-Gaussian Random Field Models

## TL;DR

This paper introduces a flexible spatial model for environmental data that captures non-Gaussian features like skewness and heavy tails, improving the understanding of complex spatial dependencies.

## Contribution

It proposes a novel scale-shape mixture of skew-normal distributions to model non-Gaussian spatial responses with asymmetric tail dependence.

## Key findings

- Model can generate various skewness and kurtosis levels
- Captures asymmetric tail dependence in spatial data
- Enhances environmental response analysis

## Abstract

In the environmental modeling field, the exploratory analysis of responses often exhibits spatial correlation as well as some non-Gaussian attributes such as skewness and/or heavy-tailedness. Consequently, we propose a general spatial model based on scale-shape mixtures of the multivariate skew-normal distribution. Intuitively, it incorporates distinct random effects to account for the spatial dependencies not explained by a simple Gaussian random field model. Importantly, the proposed model is capable of generating a wide range of skewness and kurtosis levels. Meanwhile, we demonstrate that the skewness mixing can induce asymmetric tail dependence at sub-asymptotic and/or asymptotic levels.