Is there a Julia package that calculates inequality measures like Gini Index, Theil Index, Atkinson Index, Hoover Index?
I don’t know but I’d be totally up for writing one together! This is part of my PhD topic. P.S. Atkinson is the best obviously
I am planning to use the inequality index as a constraint in a linear problem. I have not quite looked closely at Atkinson Index so could you tell me if the Atkinson index can be used in an LP?
I’ve never done linear programming, sorry. I’m more interested in the ethics side of things.
However, if you’re doing some sort of optimization, I’d just maximize social welfare and skip the inequality measure. So if you’re working with income, just maximize total income * (1 - the atkinson index for income). You can do a bit of cancellation to simplify this expression.
P.P.S. don’t pick one for the risk aversion parameter if you’re going to use the Atkinson index. Usually you’ll want a higher number; look for an estimate of mean RELATIVE risk aversion (there’s a ton of studies on this).
I have a bunch of these written up for Gini, Theil, Atkinson and a few other common measures including functions to calculate them from common distribution families, mixture models and kernel density estimates. I’ll hunt them out and post them in a gist
EDIT : code