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Pareto2(q,b) - no Crystal Ball distribution = Pareto(a, q) – a, where a = b, and q = q

Pareto equations (second kind)

This distribution is simply a standard Pareto distribution but shifted along the x-axis so that it starts at x = 0. This is most readily apparent by studying the cumulative distribution functions for the two distributions:





The only difference between the two equations is that x for the Pareto has been replaced by (x+b) for the Pareto2. In other words, using the notation above:

Pareto2(b,q) = Pareto(q,a) – a

where a = b, and q = q

Thus both distributions have the same variance and shape when a = b and q = q, but different means.


See the Pareto distribution

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