# Mapping gini index

In my model, there are 3 players, whose income is function of two arbitrary parameters. Say, P(1) = F(a,b) where 0<a<1 , 0<b<1 and P(1) is income of player 1. Similarly for other two players we have, P(2)=G(a,b) and P(3)=H(a,b). Functions F(), G() and H() are known. I have 2 questions.

1. Which is the best index to measure inequality (gini, variance or else) for such small sample size?
2. How to map gini for various values of a and b? I mean which software does this.
• If you have three numbers, why use any measure of inequality? More seriously, there is no "best" independently of purpose. Note that Gini index is a name used for several quite different indexes, depending partly on disciplines, including various related measures based on the sum of squared proportions. That's a one-line calculation in any mathematical or statistical software worthy of the name. – Nick Cox May 17 '13 at 8:07
• @NickCox by gini index i meant en.wikipedia.org/wiki/Gini_coefficient – Ashni Goyal May 17 '13 at 8:36
• Also, I am talking about mapping it. The income is dependent on two parameters which vary from 0 to 1. Hence, for each combination of a and b we will have a set of incomes , for which gini can be calculated. I wanted to calculate for , say, 100 or 1000 ponts. – Ashni Goyal May 17 '13 at 8:39
• I will b grateful if u could point towards a software which can do such mapping. Can we calculate gini in matlab ? – Ashni Goyal May 17 '13 at 8:39
• I've not read all the Wikipedia article, but on a quick glance it misses a fundamental point, the multiple meanings that can be found for Gini index in various literatures. I am sure that you can calculate your chosen index in MATLAB. Some one else should be able to give you some code if they can follow your explanation. (I can't, but even someone fluent in MATLAB would appreciate some details on your data structure.) When you say "map", do you mean as in cartography or as in a mathematical sense (e.g. a mapping from one set to another)? – Nick Cox May 17 '13 at 9:05