Validity Range of the Discrete Gaussian Change-of-Support Model and its Variant

The discrete Gaussian model is a very popular change-of-support model for estimating block grade distributions. It is designed for a stationary random function Z(x) that is regarded as the transform of a stationary random function Y(x) with Gaussian marginal. It is based on an assumption that is not fully true and thus constitutes an approximation to the exact solution. We examine the effect of this approximation on the modelling of the marginal distribution of block values of a lognormal random function. The initial discrete Gaussian model and a variant of that model are considered.