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