A SURVEY INTO ESTIMATION OF LOGNORMAL DATA

Abstract

Lognormal data are very difficult to handle because of its high variability due to the occurrence of a few high values. In geostatistics the solution calls for a data transform, such as the logarithm transform and the indicator transform. Both approaches have been used for estimating lognormal data. Lognormal kriging works on kriging the transformed data and then estimates are back-transformed into the original scale of data. Indicator kriging builds a conditional cumulative distribution function at every unsampled location and estimates are based on the conditional mean or E-type estimate. Usually back-transformed lognormal kriging estimates are mean biased and conditional means from indicator kriging are unbiased. This paper compares both approaches for 27 data sets presenting distributions with increasing positive skewness. Actually 27 exhaustive data sets have been computer generated from which stratified random samples with 90 points were drawn. Estimates were first examined for local accuracy and the associated uncertainties were checked for the proportional effect. Results show that lognormal kriging is still the best approach for lognormal data if we use an algorithm that takes into consideration correcting the smoothing effect before back-transformation. Keywords: lognormal distribution, lognormal kriging, indicator kriging, proportional effect.