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# Pareto (Power) Distribution Random Number Generator

The Pareto distribution is a two-parameter probability distribution whose PDF is given by the equation

PDF(x) = ab^{a}/x^{a+1}, x ∈ [b, ∞), a > 0

Economists often use the Pareto probability function to model the distribution of wealth, sizes of cities, and other situations in which there are many small items and fewer large items. Alternative names for model are *power distribution* and *Bradford distribution*.

The Pareto distribution has a mean of ab/(a-b) for a > 1 and a variance of

ab²/(a³ - 4a² + 5a - 2)

for a > 2. The mode, median, and skewness are given by

mode = b

median = b2

^{1/a}

skew = [(2a + 2)/(a-3)]sqrt(1 - 2/a) for a > 3.

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