Pareto (Power) Distribution Random Number Generator
The Pareto distribution is a two-parameter probability distribution whose PDF is given by the equation
PDF(x) = aba/xa+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 = b21/a
skew = [(2a + 2)/(a-3)]sqrt(1 - 2/a) for a > 3.
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