Abstract
Some specific random fields have been studied by many researchers whose finite-dimensional marginal distributions are multivariate closed skewnormal or multivariate extended skew-t, in time and spatial domains. In this paper, a necessary and sufficient condition is provided for applicability of such random field in spatial interpolation, based on the marginal distributions. Two deficiencies of the random fields generated by some well-known multivariate distributions are pointed out and in contrast, a suitable skew and heavy tailed random field is proposed. The efficiency of the proposed random field is illustrated through the interpolation of a real data.
Highlights
In recent years, random fields (RFs) have been successfully applied, as a statistical model, to the analysis of biological sequences, text and image processing, as well as many areas of computer vision and artificial intelligence
We show that the RFs generated by some versions of multivariate SN, Closed Skew-Normal (CSN) and Extended Skew-t (EST) distributions have two weakness in application to the spatial interpolation
Our findings show that definition of a RF based on multivariate CSN and EST distributions as studied by the corresponding researchers, have these two weaknesses
Summary
Random fields (RFs) have been successfully applied, as a statistical model, to the analysis of biological sequences, text and image processing, as well as many areas of computer vision and artificial intelligence. Some RFs have been defined by multivariate Skew-Normal (SN) distribution (Azzalini, 1985) [5], multivariate Closed Skew-Normal (CSN) distribution (González-Farías et al, 2004) [10], multivariate Skew-t distribution and its general form, multivariate Extended Skew-t (EST) distribution (Arellano-Valle and Genton, 2010) [3]. We show that the RFs generated by some versions of multivariate SN, CSN and EST distributions have two weakness in application to the spatial interpolation.
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