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How are kriging quantile maps calculated?

Question asked by whuber on Dec 27, 2013
Latest reply on Jan 3, 2014 by EKrause-esristaff
The help page for types of kriging surfaces seems to say that the quantile map for any quantile q (between 0 and 100%) is constructed as the sum of the prediction map and z times the standard error (SE) map where z is the qth quantile for the standard normal distribution.  This in fact is not the case for ordinary kriging when the variogram is not a pure nugget, as you can check by constructing these three maps and comparing any GA quantile map (for q differing from 50%) to the prediction and SE maps.  The discrepancies--which are both positive and negative and about correct on average--vary with location, prediction, and standard error, so this does not seem to be the result of an approximate calculation.  What is the software really computing?  What formula does it use?

(The help page echoes material from the book Using ArcGIS Geostatistical Analyst.  See especially pages 262-264.  I tested using no transformations of the data and specified variograms with no measurement error.)