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Re: AI-GEOSTATS: Distribution of Zmax-Zmin for M samples from N(0,1)?

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  • Syed Abdul Rahman Shibli
    It seems that you can extend this further to calculate a madogram for each grid density (mean absolute difference). Different grid densities, different radii,
    Message 1 of 2 , Aug 26, 2002
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      It seems that you can extend this further to calculate a madogram
      for each grid density (mean absolute difference). Different grid
      densities, different radii, ergo different madogram shapes. Each madogram
      may or may not show a range. The trick is to come up with a grid
      density that would result in a radius that is more or less equivalent
      to the range, to extract maximum interpolation data. Because the
      grid is on equal spacing, the problem is finding a range to compare to,
      and the only one available would be the global range of the data.

      Regards,

      Syed

      >Overlay a grid on a 2D distribution of random variables Z(x,y) and
      >assign all such variables to the nearest grid node. Then consider
      >the distribution of F(i,j) = (ZMAX-ZMIN)(i,j) for any grid node with
      >nearby data. For simplicity, assume that the original random variables
      >are (locally) normally distributed and that all collected at any node
      >have the same mean and standard deviation. What is the distribution
      >of F?
      >
      >My reason for asking is that I am trying to automatically select
      >a grid row and column spacing to use in grid-based surface modeling
      >and one intuitive criteria is to get a "dense enough" grid that the
      >largest ZMAX-ZMIN for any single grid node is small relative to the
      >range of Z values in the input data set. (Well, intuitive to me.)
      >Then I started wondering what I might conclude if the sampled mean
      >plus a couple of standard deviations for the population of such node
      >variables was small. And then I got confused.
      >
      >I am guessing that the distribution of F is standard problem in
      >statistics when the data are normal: Given M samples from N(0,1),
      >what is the distribution of Zmax-Zmin? But I don't have the right
      >"standard" statistics book.
      >
      >Hmmm. Maybe I am gathering information about the nugget for a data
      >set?
      >
      >Thanks,
      >
      >Steven Zoraster
      >
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