## 1944[ai-geostats] Re: question about kriging with skewed distribution

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• Mar 5, 2005
Ruben (et al)

It is true that Matheron's theory is based on no
distributional assumptions. In fact, there is no
requirement for the distribution to be the same at
every location in the study area.

The necessity for using traditional geostatistical
theory is that the 'difference between two values'
should have a common distribution for a specified
distance (and possibly direction). The form of this
distribution is irrelevant but it needs to possess a
mean and variance.

The problem lies not with the theory but with the
practice. If you have the whole 'realisation' you can
calculate the true average and variance and the shape
of each distribution is irrelevant. If you have only a
few samples, then you can only find estimates for the
means and variances at each distance.

If the underlying distribution is highly skewed then,
unless you have ideal conditions (large number of
samples, regular sampling locations), your estimate of
the variance will be unstable -- influenced by the
average of the samples included in the particular
"proportional effect" back in the 70s [search for
'relative semi-variogram'].

So, you have two potential problems:

(1) you may not get any true picture of the
semi-variogram due to the uncertainty associated with
each point exacerbated by the proportional effect;

(2) you may not wish to use an averaging technique
such as kriging on skewed samples. All of Sichel's
(mining) and much of Krige's work was motivated by the
fact that local averaging is not sensible when your
data has a coefficient of variation greater than
around 1.

The theory is terrific, witness its survival for over
40 years and its proliferation over many fields of
application. However, real life isn't so tidy at the
sharp end ;-)

Isobel
http://geoecosse.bizland.com/whatsnew.htm
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