Backtransforming rank order kriging estimates

Abstract

Kriging of raw data presenting distributions with positive skewness must be avoided because the strong infl uence of a few high values in the resulting estimates. The solution is to apply data transformation, which changes the shape of original distribution into a symmetric distribution. Kriging of transformed data is performed and then back-transformed to the original scale of measurement. In this paper, we examine the uniform score transform that results in a uniform distribution. Ordinary kriging estimates of uniform score data results in a bell-shaped distribution, since the tails of the distribution are lost in the estimation process because of the smoothing effect. The back-transformation of this bell-shaped distribution result in biased estimates. Therefore, the solution proposed in this paper is to correct the smoothing effect of the rank order kriging estimates before transforming them back to the scale of raw data. Results showed this algorithm is reliable and back-transformed estimates are unbiased in relation to the sample data.