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AI-GEOSTATS: Re: Lognormal distributions.

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  • Digby Millikan
    Hello everyone, Here is a summary of my question about information on lognormal distributions in mining. ... Jeff Myers wrote: I can t help on the reference,
    Message 1 of 1 , Jan 8, 2003
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      Hello everyone,

      Here is a summary of my question about information on lognormal
      distributions in mining.

      > Hello,
      >
      > I was wondering if someone could give me recommendations on
      > 'Lognormal Distributions: Theory and Applications' Edwin L. Crow
      > for one interested in theoretical and practical aspects of nonlinear
      > (lognormal) geostatistics.
      >
      > Regards Digby Millikan B.Eng
      >

      Jeff Myers wrote:

      I can't help on the reference, but I would offer a friendly reminder that
      the lognormal sample distribution could be a result of incorrect sampling
      and subsampling procedures. If the sample support (mass/volume) at either
      the sample or subsample (laboratory) level is too small, chances are good
      that your distribution will look lognormal. Applying Pierre Gy's sampling
      theory may help normalize the distribution. In my training courses,
      attendees sample a material with different-sized sampling devices. Those
      with smaller devices produce highly skewed histograms whereas those with
      larger devices get normal-looking histograms. If you'd like, I can send you
      a paper that describes an actual application of this sample material to the
      design of a sampling program for explosives in soils at the Pueblo Chemical
      Depot (Colorado), where particulate materials (soils) were being sampled.
      Both sample support and the distributional assumption were key issues. The
      paper also contains histograms showing the distributions obtained from
      different sample supports.

      Best Regards,

      Jeff Myers

      I've attached a copy of the paper for you. Enjoy. FYI, I've also attached
      a description of the training.

      I started life as a mining engineer/geostatistician. I learned in western
      US gold mines that lab results were highly speculative due to the
      fundamental sampling error. If your data aren't representative of the
      orebody, you are trying to model an illusion. As I write to the ai-geostats
      list periodically, you can't contour yourself out of something you sampled
      yourself into. If your sample data don't reflect reality, even your
      statistician doesn't know for sure.

      Krige's relationship tells us that we have a continuum from point samples to
      the whole deposit. Point samples have the highest variability (related to
      Gy's theory). The deposit has no variance (it is what it is). Sub-deposit
      supports (blocks, bulk samples, etc.) have variability which, at some
      supports, follow normal distributions. The problem is that these support
      volumes may not be practical for sampling. However, it is typical for
      precious metals deposits to take samples that have inappropriately small
      support volumes. Thus, it is usually possible to improve your estimation by
      adjusting the sampling approach to reduce the sampling error as much as is
      feasible. Ironically, most people don't do it.....

      Jeff


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