Abstract
Fractal properties of the Pareto probability distribution are used to generalize “the 20/80 law.” The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The generalp100/q100 law in probabilistic form is defined withq as a function ofp, wherep is the population proportion andq is the proportion of total value. Using the Pareto distribution, thep100/q100 law in fractal form is derived with the parameterq being a fractal, whereq unexpectedly possesses the scale invariance property. The 20/80 law is a special case of thep100/q100 law in fractal form.
Thep100/q100 law in fractal form is applied to petroleum fieldsize data to obtainp andq such thatp100% of the oil fields greater than any specified scale or size in a geologic play account forq100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractalq are extremely close to the empirical percentages from the data using the statisticq. Also, the empirical scale invariance property of the statisticq for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractalq.
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Crovelli, R.A. The generalized 20/80 law using probabilistic fractals applied to petroleum field size. Nat Resour Res 4, 233–241 (1995). https://doi.org/10.1007/BF02257575
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DOI: https://doi.org/10.1007/BF02257575