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AI-GEOSTATS: sum: generating skewed distributions

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  • William Thayer
    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
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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 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
      301 Plainfield Road, Suite 350
      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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