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Lognormal data. RE: AI-GEOSTATS: Variogram behaviour

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  • Ruben Roa
    ... variogram, but with OK a poor variogram ... distance methods, though with ... result in highly erroneous estimates, ... percentage error in your estimate.
    Message 1 of 2 , Mar 16, 2001
      >===== Original Message From "Digby Millikan" <digbym@...> =====
      >Hello,
      > I have always lead the belief that it is worth while cleaning up a
      variogram, but with OK a poor variogram
      >model for normally distributed data will give superior results than inverse
      distance methods, though with
      >lognormally distributed data fitting of a model to a poor variogram can
      result in highly erroneous estimates,
      >as for example the percentage error in your sill will result in an equal
      percentage error in your estimate.
      >Diverging from the topic a bit a method I preferred for lognormal data with
      poor variograms is to use inverse
      >distance or ordinary kriging with a topcut calculated as the topcut which
      will give you an arithmetic mean
      >equal to the sichel t estimator (an estimate of the true mean of a lognormal
      population). That way overestimation
      >due to lognormality is avoided without resorting to lognormal kriging. I
      beleive their may also be a method for
      >estimating the mean of a multiguassian distribution.
      >Regards Digby Millikan.

      Regarding lognormal data, if you are only interested in the mean of the
      regionalized variable and its confidence interval whithin the region, and not
      in the spatial mapping itself, you can just use the MLE estimator of the
      lognormal mean, the (Finney-)Sichel estimator that you mentioned, to obtain
      the point estimate, and the theory and tables in Land (1975, Tables of
      confidence limits for linear functions of the normal mean and variance,
      Selected Tables in Mathematical Statistics, vol. III, Am. Math. Soc.
      Providence, pages: 385-419) to obtain the asymmetric confidence interval. This
      solution might not be popular among members of the list, however, since it
      involves abandoning the spatial analysis.

      Ruben


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    • Isobel Clark
      ... I am unfamiliar with these tables as most practitioners that I know us Sichel s original tables (or mine). Computational methods are discussed fully in my
      Message 2 of 2 , Mar 17, 2001
        > ..... you can just use the MLE estimator of the
        > lognormal mean, the (Finney-)Sichel estimator that
        > you mentioned, to obtain
        > the point estimate, and the theory and tables in
        > Land (1975, Tables of
        > confidence limits for linear functions of the normal
        > mean and variance,
        > Selected Tables in Mathematical Statistics, vol.
        > III, Am. Math. Soc.
        > Providence, pages: 385-419) to obtain the asymmetric
        > confidence interval.
        I am unfamiliar with these tables as most
        practitioners that I know us Sichel's original tables
        (or mine). Computational methods are discussed fully
        in my 1987 paper in the SAIMM, cf.
        http://uk.geocities.com/drisobelclark/resume/Publications.html

        > This
        > solution might not be popular among members of the
        > list, however, since it
        > involves abandoning the spatial analysis.
        Ruben, I think you do all of us a great injustice with
        this statement. The members of this list are here
        because they want free communication and to find the
        best solutions to their problems.

        There are sectors of the geostatistical community who
        are rabidly opposed to classical statistical
        approaches and other non-geostat methods. However, I
        have yet to see them contribute to the discussions in
        this list.

        Isobel Clark
        (self styled sceptic)



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