Measures of inequality ----------------------
^ineq^ varname [^if^ exp] [^in^ range] [weight] [, ^n^umeq ^by(^byvarlist^) gens^im^(^newvar^) gene^nt^(^newvar^)^ ^gend^iss^(^newvar^)^ tabdisp_options ]
^ineq^ treats varname as an additive variable -- that is, assumes totals make sense and that no negative values are present in the data specified -- and calculates three measures of inequality.
Given n values of y, scale to proportions p = y / SUM y. Then
Simpson's index is SUM p^^2. If one value of p is 1, and the others thus all 0, this index takes on a maximum value of 1. If all p are 1 / n, it takes on a minimum value of 1 / n.
Shannon entropy is - SUM p ln p = SUM p ln 1/p. If one value of p is 1, this index takes on a minimum value of 0. If all p are 1 / n, it takes on a maximum value of ln n.
Dissimilarity index is (1 / 2) SUM | p - 1 / n |. If one value of p is 1, this index takes on a maximum value of (n - 1) / n. If all p are 1 / n, it takes on a minimum value of 0.
These measures are known under a variety of names, and a variety of related guises, in different fields.
fweights and aweights are allowed.
^by(^byvarlist^)^ specifies that calculations should be performed separately for groups defined by byvarlist.
^numeq^ specifies that Simpson's index and entropy are to be converted to number equivalents, namely 1 / Simpson's index and exp(entropy).
^gensim( )^, ^genent( )^ and ^gendiss( )^ specify that new variables should be generated containing values of the three measures.
tabdisp_options are options of ^tabdisp^ controlling the tabulation of results. The default is ^format(%4.3f)^.
. ^ineq income^
Nicholas J. Cox, University of Durham, U.K. n.j.cox@@durham.ac.uk
Also see --------
On-line: help for @tabdisp@