Pareto Distribution
X ~ Pareto(x_m, α)
Power-Law / Heavy-Tailed Family • Published July 31, 2026
The 80/20-rule distribution: history from Vilfredo Pareto's 1896 land-ownership observation, the continuous counterpart to the already-published Zipf's law, a stark warning that the mean and variance can silently fail to exist depending on the tail index, a closed-form maximum-likelihood estimator for the shape parameter, and simulation via a log-transform of the Exponential.
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About This Reference Sheet
The 80/20-rule distribution: history from Vilfredo Pareto's 1896 land-ownership observation, the continuous counterpart to the already-published Zipf's law, a stark warning that the mean and variance can silently fail to exist depending on the tail index, a closed-form maximum-likelihood estimator for the shape parameter, and simulation via a log-transform of the Exponential.
Support
x ∈ [x_m, ∞)
Parameters
x_m > 0 (minimum/scale), α > 0 (shape / tail index)