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Monte Carlo simulations of product distributions and contained metal estimates

January 1, 2013

Estimation of product distributions of two factors was simulated by conventional Monte Carlo techniques using factor distributions that were independent (uncorrelated). Several simulations using uniform distributions of factors show that the product distribution has a central peak approximately centered at the product of the medians of the factor distributions. Factor distributions that are peaked, such as Gaussian (normal) produce an even more peaked product distribution. Piecewise analytic solutions can be obtained for independent factor distributions and yield insight into the properties of the product distribution. As an example, porphyry copper grades and tonnages are now available in at least one public database and their distributions were analyzed. Although both grade and tonnage can be approximated with lognormal distributions, they are not exactly fit by them. The grade shows some nonlinear correlation with tonnage for the published database. Sampling by deposit from available databases of grade, tonnage, and geological details of each deposit specifies both grade and tonnage for that deposit. Any correlation between grade and tonnage is then preserved and the observed distribution of grades and tonnages can be used with no assumption of distribution form.

Publication Year 2013
Title Monte Carlo simulations of product distributions and contained metal estimates
DOI 10.1007/s11053-013-9206-8
Authors Mark E. Gettings
Publication Type Article
Publication Subtype Journal Article
Series Title Natural Resources Research
Index ID 70188867
Record Source USGS Publications Warehouse
USGS Organization Geology, Minerals, Energy, and Geophysics Science Center