## AI-GEOSTATS: sum: generating skewed distributions

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• The replies I received to my request appear below, along with the original request for help. Thanks to those who replied. Original request: I am interested in
Message 1 of 1 , Apr 15, 2002
The replies I received to my request appear below, along with the original
request for help. Thanks to those who replied.

Original request:
I am interested in comparing different estimators of spatial means. Any
suggestions or approaches on how to generate a 2-D, autocorrelated, skewed
distribution that exhibits non-stationary mean and variance?

Replies:
How about using sasim.f in GSLIB to generate several non-conditional
realizations of a property using simulated annealing? You can
specify:

1. a user-defined histogram, which may be as skewed as you wish, and
2. a non-stationary power law variogram (fractional Brownian motion)
to approximate a variable with a drift component.

Hope this helps.

Syed

Bill, just a quick idea. Build a variogram with a trend in it, no sill, and
use it in a Gaussian simulator (e.g., sgsim). Make the simulation in
standard normal space and then use the GSLIB trans program to transform it
to any raw-space skewed distribution you want. The transformation is
quantile preserving so should not change the autocorrelation, but I would
double-check the results. This process will certainly generate a correlated
field with a skewed distribution and non-stationary mean. I'm not exactly
sure how you want the variance to be non-stationary and that may be harder
to do. Non-linear transforms can produce a prorportional effect (variance
is a function of the simulated value), but they generally don't preserve the
variogram.

good luck

Sean

Without giving it too much thought, I wonder if just generating a
stationary autocorrelated normal field, Zn and "back-transforming" it to
produce a lognormal field, Zl wouldn't work? Because the kriging variance
comes into both the mean and variance of the back-transformed variable, it
should
be non-stationary.

Yetta

Yes. Generate a Gaussian random field, add a deterministic trend
surface, and take the exponent or a power transform of the sum.

Edzer
**************************************************
William C. Thayer, P.E.

Environmental Science Center
Syracuse Research Corporation
Syracuse, NY 13212
phone: (315) 452-8424
fax: (315) 452-8440
email: thayer@...
web: http://esc.syrres.com/
http://esc.syrres.com/geosem/
**************************************************

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