theil {binsmooth}

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.)

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.

Value

Returns the Theil index T.

Author(s)

David J. Hunter and McKalie Drown

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

# 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