gini {binsmooth}

Estimate the Gini coefficient

Description

Estimates the Gini coefficient from a smoothed distribution.

Usage

gini(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 Gini coefficient can be computed from a cumulative distribution function F(x) by the integral

G = 1 - \frac{1}{\mu}\int_0^\infty (1-F(x))^2 \, dx

where \mu is the mean of the distribution.

Value

Returns the Gini coefficient G.

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)
gini(stepfit)
gini(splinefit) # More accurate