Concept# Pareto interpolation

Summary

Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution. It is used in economics when analysing the distribution of incomes in a population, when one must base estimates on a relatively small random sample taken from the population.
The family of Pareto distributions is parameterized by

- a positive number κ that is the smallest value that a random variable with a Pareto distribution can take. As applied to distribution of incomes, κ is the lowest income of any person in the population; and
- a positive number θ the "Pareto index"; as this increases, the tail of the distribution gets thinner. As applied to distribution of incomes, this means that the larger the value of the Pareto index θ the smaller the proportion of incomes many times as big as the smallest incomes.

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