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
K =
\left(
\frac{P_b - P_a}
{ \frac{1}{a^{\theta}} - \frac{1}{b^{\theta}}}
\right) ^{ \frac{1} {\theta}}
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\theta \; = \;
\frac{\log(1-P_a) - \log(1-P_b)}
{\log(b) - \log(a)}
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