binsmooth (version 0.2.2)

theil: Estimate the Theil index

Description

Estimates the Theil index from a smoothed distribution.

Usage

theil(binFit)

Arguments

binFit

A list as returned by splinebins, stepbins, or rsubbins. (Alternatively, a list containing a PDF of non-negative support, its CDF, and an upper bound for the support of the PDF.)

Value

Returns the Theil index \(T\).

Details

For distributions of non-negative support, the Theil index can be computed from a probability density function \(f(x)\) by the integral $$T = \int_0^\infty f(x) \frac{x}{\mu} \ln\left(\frac{x}{\mu}\right) \, dx$$ where \(\mu\) is the mean of the distribution.

References

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/

Examples

# NOT RUN {
# 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
# }