What is wrong with kurtosis in Geostatistical Analyst?

[MilanDjordjevic]

When I compare values of descriptive statistics of my data from Excel and Minitab with statistics from Geostatistical Analyst (Histogram) there is a huge difference.

results from Excel and Minitab:
Variable  Skewness  Kurtosis
C1           -0.00     -0.82
C2           -0.82     -0.22
C3           -0.49     -1.03
C4           -0.21      0.49
C5           -1.45      2.10
C6           -0.26     -0.29

results from Geostatistical Analyst - Histogram:
Variable  Skewness  Kurtosis
C1            0.00      2.16
C2           -0.78      2.69
C3           -0.49      1.96
C4           -0.20      3.38
C5           -1.40      4.83
C6           -0.23      2.66

Those results shown in Geostatistical Analyst - Histogram are for the same data with no transformation performed. Why is there any difference?

[DanPatterson_Retired]

check the actual formulae being used, there are variants, have a look at this as well
http://resources.arcgis.com/gallery/file/geoprocessing/details?entryID=BDF21676-1422-2418-34E6-A29C6...

[EricKrause]

We use a simple kurtosis formula in Geostatistical Analyst.  The formula is the fourth moment divided by the square of the second moment.  We do not correct for small samples or calculate excess kurtosis.

It appears that the KURT function in Excel calculates excess kurtosis and corrects for small sample sizes.  In general, the difference between these two calculations should be approximately 3.  You can see from your data that if you add 3 to the Excel values, you will get close to the ArcGIS values (the remaining difference is due to small sample corrections in Excel).