theil {binsmooth} | R Documentation |
Estimates the Theil index from a smoothed distribution.
theil(binFit)
binFit |
A list as returned by |
For distributions of non-negative support, the Theil index can be computed from a probability density function f(x) by the integral
T = \int_0^∞ f(x) (x/μ) \ln(x/μ) \, dx
where μ is the mean of the distribution.
Returns the Theil index T.
David J. Hunter and McKalie Drown
Paul T. von Hippel, David J. Hunter, McKalie Drown. Better Estimates from Binned Income Data: Interpolated CDFs and Mean-Matching, Sociological Science, November 15, 2017. https://www.sociologicalscience.com/articles-v4-26-641/
# 2005 ACS data from Cook County, Illinois binedges <- c(10000,15000,20000,25000,30000,35000,40000,45000, 50000,60000,75000,100000,125000,150000,200000,NA) bincounts <- c(157532,97369,102673,100888,90835,94191,87688,90481, 79816,153581,195430,240948,155139,94527,92166,103217) stepfit <- stepbins(binedges, bincounts, 76091) splinefit <- splinebins(binedges, bincounts, 76091) theil(stepfit) theil(splinefit) # More accurate