The beta distribution for categorical variables at different support

Abstract

Categorical variables are commonly encountered in mathematical geology. The categories may represent facies, rock types, soil types or some other discrete variable. These categories are mutually exclusive at the small data support; however, they become mixed as scale increases; the facies indicators become proportions at larger support. Geostatistical simulation at a fixed support requires a model for the probability distribution at the support being considered. The first and second order moments of the univariate and bivariate scale-dependent facies proportion distribution may be predicted by well established scaling laws. The shape of the scale-dependent multivariate distribution of facies proportions may be modeled by the ordinary Beta distribution. This has widespread application in geostatistical modeling of geological sites. © 2008 Springer-Verlag Berlin Heidelberg.