AI-GEOSTATS: Re: Lognormal distributions.
- Hello everyone,
Here is a summary of my question about information on lognormal
distributions in mining.
> Hello,Jeff Myers wrote:
> 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
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.
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.....
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