New Method of Fitting Pareto–Lognormal Size-Frequency Distributions to Worldwide Cu and Zn Deposit Size Data

Abstract

Earlier methods of fitting Pareto–lognormal distributions to large samples of worldwide metal deposit size data are improved by using a sliding window method for estimating upper-tail Pareto coefficients and constructing best-fitting lognormal Q–Q plots with their corresponding probability-density curves. Lower-tail Pareto distributions are fitted to some extent as well. Copper and Zn deposits of the world are taken as example in this paper. Three principal statistical laws resulting in the basic lognormal with two Pareto tails are thought to underlie the generation of Pareto–lognormals for amounts of metal in primarily hydrothermal ore deposits. Historical trends in mining and exploration are thought to create an excess of smaller deposits with respect to the basic lognormal that decreases steadily with increasing deposit size until it changes into a deficit slightly before median size is reached. This deficit decreases for the largest metal deposit sizes for which the upper-tail Pareto and extrapolated basic lognormal show similar size frequencies again. The Pareto–lognormal model can also be used to describe metal size-frequency distributions for smaller geographically coherent regions on the continents. A new version of the original model of de Wijs is considered to help explain why regional Pareto–lognormal distributions with lesser logarithmic variances and Pareto coefficients can be combined to form worldwide size-frequency distributions of the same type.