Introducing a Stationary Skew-Gaussian Random Field

The Gaussian random field is commonly used to analyze spatial data. One of the important features of this random field is having essential properties of the normal distribution family, such as closure under linear transformations, marginalization and conditioning, which makes the marginal consistency condition of the Kolmogorov extension theorem. Similarly, the skew-Gaussian random field is used to model skewed spatial data. Although the skew-normal distribution has many of the properties of the normal distribution, in some definitions of the skew-Gaussian random field, the marginal consistency property is not satisfied. This paper introduces a stationery skew-Gaussian random field, and its marginal consistency property is investigated. Then, the spatial correlation model of this skew random field is analyzed using an empirical variogram. Also, the likelihood analysis of the introduced random field parameters is expressed with a simulation study, and at the end, a discussion and conclusion are presented.