# Pareto interpolation

**Pareto interpolation** is a nonlinear method of

interpolation to find the

median of a set of data. It is used in

economics when analysing income figures. It assumes that the data fits a curve known as the

Pareto distribution.

The median is given by

where parameters κ and θ are given by:

and

where

*a* = lower limit of the category containing the median

*b* = upper limit of the category containing the median

*P*_{a} = proportion of the distribution that lies below the lower limit

*P*_{b} = proportion of the distribution that lies below the upper limit