The power-law distribution of cumulative coal production

The coal industry is dominated by the largest mines, with 1% of coal mines in the U.S. being responsible for 65% of the coal cumulatively produced. We show that this "heavy tail" can be well approximated by a power law, where mine-level cumulative production is inversely proportionate to distributional rank. Maximum likelihood and regression-based procedures estimate the counter-cumulative power-law parameter to be less than one, indicating there is no well-defined mean or variance for cumulative production. Goodness of fit tests indicate the power-law is a better fit to the data than other competing distributions, including the lognormal. (C) 2019 Elsevier B.V. All rights reserved.