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Pareto on Lognormal Q-Q plot
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Log10 (Amount of Metal)
Fig. 10.9 Two distributions of Fig. 10.8 re-plotted as lognormal Q - Q plot (Source Agterberg
2007 , Fig. 1b)
because as frequency for the lognormal approaches 0 for decreasing amount of
metal, the corresponding Pareto frequency approaches
. The number of oil fields
containing more than a given amount of oil can be modeled by means of the Pareto
distribution, as demonstrated by several authors including Drew et al. ( 1982 ) and
Crovelli ( 1995 ).
Singer and Menzie ( 2010 ) used the lognormal distribution as a benchmark for
the modeling of worldwide metal resources. Agterberg and Divi ( 1978 ) developed a
two-dimensional lognormal model for copper, lead and zinc ore deposits in the
Canadian Appalachian region. On the other hand, Turcotte ( 1997 ) provides various
examples of successful fitting of the Pareto to various metal resource data sets.
These examples include log-log plots of grade versus cumulative production of
mercury, lode gold and copper in the United States originally established by Cargill
( 1981 ) and Cargill et al. ( 1980 , 1981 ). Respective merits of lognormal and Pareto
size-modeling already were investigated in Chap. 4 for copper deposits in the
Abitibi area on the Canadian Shield. In the Abitibi copper hindsight study, both
models were applicable although the Pareto had the advantage in predicting prop-
erties of size frequency distributions of amounts of copper ore that was to be
discovered later.
Freiling ( 1966 ) made a direct comparison of lognormal and Pareto distributions
showing that the tails of these distributions are very different. However, extensive
testing of the two models on mass-size distributions led him to the conclusion that
available data were not sufficient to distinguish between lognormal and power-law
distributions in practice.
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