Statistical Distribution Laws for Metallic Mineral Deposit Sizes

Given that expanding industrial societies rely on the continuing supply of metallic raw materials, it is of interest to be able to generate estimates of the likely magnitude of undiscovered metal resources. Statistical predictions of this kind require that one knows the frequency distribution of the metal content (or tonnage) of mineral deposits. The distribution of metal content among deposits of different sizes may be treated empirically (i.e., without explicit formulation of a density function), or formally, starting from a density function that is known to represent the distribution of metal in known deposits. The empirical approach has been applied to the prediction of undiscovered resources of some metals, most notably copper. The focus here is on the formal approach, which may be simpler and more general than the empirical one. It has long been suspected that the distribution of metal tonnages is heavy-tailed, in the sense that a relatively few very large deposits are likely to contain much of the metal endowment. There is, however, uncertainty about the precise nature of the distribution of metal tonnages. Lognormal and power law models have been proposed. Under some conditions, which are examined here, the choice of one or the other of these two models may result in widely diverging estimates of the likely magnitude and distribution of undiscovered resources. However, a detailed statistical analysis of the available deposit tonnage data for 20 metals reveals that it is not possible to decide between the two models. Using conservative significance levels, both models fit the data equally well. Two different procedures are used to attempt to decide whether either of the two models is more plausible: likelihood ratio tests and power law fits to lognormally distributed synthetic data sets that mimic the natural data sets. Neither of the two procedures can detect any preference for one or the other of the two models, for any of the metals discussed here. This uncertainty may arise from the relatively small sizes of the samples available, which are limited to known and reasonably well-characterized metallic mineral deposits. There is at present no statistical justification to choose between a lognormal and a power law description of metal distribution in mineral deposits. This uncertainty should be kept in mind when preparing, and interpreting, estimates of the magnitude of undiscovered mineral resources.