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The coal industry is dominated by the largest mines, with 1% of coal mines in the US being responsible for 65% of cumulative production. This provides evidence that cumulative coal production may be well approximated by a

power law, where the amount of production is inversely proportionate to the 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 one-parameter distributions. Additionally, the powerlaw …