  Measuring the concentration of random variables is a fundamental concept in
probability and statistics. Here, we explore a type of concentration measure
for continuous random variables with bounded support and use it to provide a
notion of stochastic order by concentration. We give an application to the Beta
family of distributions, and specifically to the one-parameter subfamily with
constant mean. This leads to using U.S. household income data to fit
generalized Beta distributions and offers a new measure of income
concentration.
