Compute the Gini Coefficient

Description

Computes the Gini coefficient based on (possibly weighted) sample data

Usage

 gini(x,  weights=rep(1,length=length(x)))

Arguments

Details

Gini is the Gini coefficient, a common measure of inequality within a distribution. It is commonly used to measure income inequality. It is defined as twice the area between the 45 degree line and a Lorenz curve, where the Lorenz curve is a graph describing the share of total income T accruing to the poorest fraction p of the population.

In typical use the values of x are the incomes of individuals from a survey and the weights are the corresponding survey weights. If the values of x are the mean incomes within income classes and the weights weights are the corresponding population proportions within those classes, the function computes an estimate of the Gini coefficient of the underlying income distribution.

Value

the Gini coefficient (between 0 and 1).

Author(s)

Mark S. Handcock handcock@stat.ucla.edu

Source

Relative Distribution Methods in the Social Sciences, by Mark S. Handcock and Martina Morris, Springer-Verlag, Inc., New York, 1999. ISBN 0387987789.

References

Relative Distribution Methods in the Social Sciences, by Mark S. Handcock and Martina Morris, Springer-Verlag, Inc., New York, 1999. ISBN 0387987789.

Divergent Paths: Economic Mobility in the New American Labor Market, Russell Sage Foundation, New York, June 2001 Annette D. Bernhardt, Martina Morris, Mark S. Handcock and Marc Scott.

Measurement of Inequality, by F. A. Cowell, in A. B. Atkinson / F. Bourguignon (Eds): Handbook of Income Distribution, Amsterdam, 2000.

Measuring Inequality, by F. A. Cowell, Prentice Hall/Harvester Wheatshef, 1995.

See Also

reldist, nls

Examples

# generate vector (of incomes)
x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)
# compute Gini coefficient
gini(x)
# generate a vector of weights.
w <- runif(n=length(x))
gini(x,w)
#
# Compute the inequality in income growth for the recent cohort of the
# National Longitudinal Survey (NLS) initiated in 1979.
#
library(reldist)
data(nls)
help(nls)
# Compute the wage growth
y <- exp(recent$chpermwage)
# Compute the unweighted estimate
gini(y)
# Compute the weighted estimate
gini(y,w=recent$wgt)

Permanent wage growth in two cohorts of the NLS

Description

These data are from two cohorts of the National Longitudinal Survey (NLS) initiated in 1966 and 1979. The cohorts are referred to as the ‘original’ and the ‘recent’ cohort, respectively. The data represents the permanent wage growth of each individual in the cohort from age 16 through 36. This was used in Handcock and Morris (1999) and Bernhardt, Morris, Handcock and Scott (2001) to study the question of wage mobility. A development of the estimation of these permanent wages and their relevance to the study of wage mobility is given in Handcock and Morris (1999). For the purposes of this reldist package, we can regard the permanent wages as measurements on two groups that we wish to compare.

The data set is comprised of two data.frames called ‘original’ and ‘recent’. Each has three columns: chpermwage: the change in permanent wages (in log-dollars), endeduc: the final achieved educational level (in years), and wgt: the sample weight.

Usage

 data(nls)

Source

Relative Distribution Methods in the Social Sciences, by Mark S. Handcock and Martina Morris, Springer-Verlag, Inc., New York, 1999. ISBN 0387987789.

References

Relative Distribution Methods in the Social Sciences, by Mark S. Handcock and Martina Morris, Springer-Verlag, Inc., New York, 1999. ISBN 0387987789.

Divergent Paths: Economic Mobility in the New American Labor Market, Russell Sage Foundation, New York, June 2001 Annette D. Bernhardt, Martina Morris, Mark S. Handcock and Marc Scott.

See Also

reldist

Annual Precipitation in US Cities

Description

The average amount of precipitation (rainfall) in inches for each of 70 United States (and Puerto Rico) cities.

Usage

data(precipitation)

Format

A named vector of length 70.

Details

This is a clone of the precip R dataset to avoid a bug in R.

Source

Statistical Abstracts of the United States, 1975.

References

McNeil, D. R. (1977) Interactive Data Analysis. New York: Wiley.

Examples

require(graphics)
data(precipitation)
dotchart(precipitation[order(precipitation)], main="precipitation data")
title(sub = "Average annual precipitation (in.)")

Inference for Relative Distributions

Description

Estimate and graph relative distribution and density functions for continuous or discrete data.

Usage

reldist(y, yo=FALSE, ywgt=FALSE,yowgt=FALSE,
  show="none", decomp="locadd",
  location="median", scale="IQR",
  rpmult=FALSE, 
  z=FALSE, zo=FALSE,
  smooth = 0.35, 
  quiet = TRUE, 
  cdfplot=FALSE,
  ci=FALSE,
  bar="no",
  add=FALSE,
  graph=TRUE, type="l",
  xlab="Reference proportion",ylab="Relative Density",yaxs="r",
  yolabs=pretty(yo), yolabslabs=NULL, 
  ylabs=pretty(y), ylabslabs=NULL,
  yolabsloc=0.6, ylabsloc=1, 
  ylim=NULL, cex=0.8, lty=1,
  binn=5000,
  aicc=seq(0.0001, 5, length=30),
  deciles=(0:10)/10,
  discrete=FALSE,
  method="Bayes",
  y0=NULL,
  control = list(samples = 4000, burnin = 1000),
  ...)

Arguments

Value

Note

Most of the code is for the plotting and tinkering. The guts of the method are forming the relative data at the top. The rest is a standard fixed interval density estimation with a few bells and whistles.

References

For more examples see the tech report

Mark S. Handcock and Eric Mark Aldrich Applying Relative Distribution Methods in R University of Washington CSSS Working Paper No. 27, Available at SSRN: doi:10.2139/ssrn.1515775.

Z. I. Botev, J. F. Grotowski and D. P. Kroese Kernel Density Estimation Via Diffusion Annals of Statistics, 2010, Volume 38, Number 5, Pages 2916-2957.

M. Wand and J. C. F. Yu Density Estimation via Bayesian Inference Engines AStA Advances in Statistical Analysis, 2021, doi:10.1007/s10182-021-00422-8.

Examples

#
# First load the data.
#

data(nls, package="reldist")

#
# A simple example comparing permanent wages of the original to the
# recent cohort in the NLS.  See H&M (1999) for details.

reldist(y=recent$chpermwage,yo=original$chpermwage,method="bgk")

#
# A more sophisticated version of the same.
#

reldist(y=recent$chpermwage, yo=original$chpermwage,
        yowgt=original$wgt, ywgt=recent$wgt,      
        bar=TRUE,                                   
        smooth=0.1, method="bgk",                             
        yolabs=seq(-1, 3, by=0.5),                 
        ylim=c(0, 3.0),cex=0.8,                   
        ylab="Relative Density",                 
        xlab="Proportion of the Original Cohort")

#
# A CDF version.
#

reldist(y=recent$chpermwage, yo=original$chpermwage,
    yowgt=original$wgt, ywgt=recent$wgt,      
    cdfplot=TRUE,                               
    smooth=0.4,                              
    yolabs=seq(-1,3,by=0.5),                 
    ylabs=seq(-1,3,by=0.5),                  
    cex=0.8,                                 
    method="bgk",                             
    ylab="proportion of the recent cohort",  
    xlab="proportion of the original cohort")

Internal reldist Objects

Description

Internal reldist functions.

Usage

entropy(x,xo=FALSE)

Arguments

Details

Most of these are not to be called by the user.

Value

If xo is given, the relative entropy (or Kullback-Liebler divergence) of the first to the second argument is calculated. Otherwise the entropy of the distribution specified by x.

See Also

reldist

Relative distribution plot to a Standard Normal

Description

resplot produces a relative distribution of the values to a standard normal.

Graphical parameters may be given as arguments to resplot.

Usage

resplot(x,
       standardize=TRUE,
       xlab="Gaussian Cumulative Proportion",
       method="Bayes",
       ...)

Arguments

Value

A list with components summarizing the relative distribution. See reldist for the details.

See Also

reldist.

Examples

y <- rnorm(2000)
resplot(y, method="bgk")
data(precipitation)
resplot(precipitation, ylab = "Precipitation [in/yr] for 70 US cities", method="bgk")

Weighted Interquartile range

Description

Compute weighted Interquartile range (iqr)

Usage

wtd.iqr (x, na.rm = FALSE, weight=NULL)

Arguments

Details

Uses a simple algorithm based on sorting.

Value

Returns an empirical interquartile range from a weighted sample.

Weighted Quantiles

Description

Compute weighted quantile

Usage

wtd.quantile (x, q=0.5, na.rm = FALSE, weight=NULL)

Arguments

Details

Uses a simple algorithm based on sorting.

Value

Returns an empirical q quantile from a weighted sample.