Robust Location Measures for Heavy-Tailed Data

Income data can be modeled by heavy-tailed distributions, which carry a significant probability measure (weight) in their tails. For such data, the sample mean is not a representative measure of the income of an average person.

Compare performance of the sample mean and some robust measures of location using US income data from a census survey.

The mean is not a representative measure of the typical income.

The median gives the income of the person in the middle of the income distribution.

Discarding the top 5% of earners gives a better picture of the life of an average person.

Instead of discarding data, the sample can be censored.

Estimate the income for an average person in the bottom half of the income distribution.

Show the means with the income histogram.