Porphyry Grade-Tonnage Distributions: A Computational Reproduction, Joint-CDF Audit, and Model-Selection Study

This working paper presents a controlled computational analysis of the U.S. Geological Survey’s 2025 global database of porphyry copper deposits and prospects. A strict parse of the source data produces 2,394 records and 33 fields. After requiring positive scalar values for reported ore tonnage and copper grade, and resolving one duplicate identity, the canonical analysis population contains 851 deposits. The primary model is the empirical joint distribution of reported copper grade and ore tonnage. Median reported tonnage is 167.942 million tonnes, and median copper grade is 0.390%. Raw correlation is nearly zero, while logarithmic and rank-based measures indicate modest negative dependence. The paper calculates a lower-orthant empirical joint cumulative distribution function, verifies all tested values against the Fréchet–Hoeffding bounds, and corrects impossible joint-probability results inherited from an earlier grade-tonnage study. Alternative lognormal, gamma, Weibull, copula and fat-tail representations are evaluated as approximations rather than treated as established generating laws. Copper-equivalent grades and a stylized project-economics simulation are retained as explicit sensitivity models because their results depend on prices, recoveries, payabilities, reporting completeness and upper-tail observations. The resulting framework provides a reproducible method for ranking reported deposits jointly by grade and tonnage. It describes the known global inventory; it is not a reserve estimate, an individual-deposit cutoff-grade curve, a mine valuation or a discovery-probability model.