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

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  • Steve Zoraster
    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
    Message 1 of 2 , Aug 26, 2002
      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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    • 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 2 of 2 , Aug 26, 2002
        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
        >
        >--
        >* To post a message to the list, send it to ai-geostats@...
        >* As a general service to the users, please remember to post a summary of any
        useful responses to your questions.
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        "unsubscribe ai-geostats" followed by "end" on the next line in the message
        body. DO NOT SEND Subscribe/Unsubscribe requests to the list
        >* Support to the list is provided at http://www.ai-geostats.org

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