**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:

Pareto: | F(x)=1-\Big(\frac{a}{x}\Big)^{\theta} |

Pareto2: | F(x)=1-\Big(\frac{b}{x+b}\Big)^{q} |

The only difference between the two equations is that x for the Pareto has been replaced by (x+b) for the Pareto2.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.

#### Uses

See the Pareto distribution