Description Usage Arguments Details Value Author(s) References See Also Examples
Compute the Gini coefficient, the most commonly used measure of inequality.
1 2 
x 
a vector containing at least nonnegative elements. The result will be 
n 
a vector of frequencies (weights), must be same length as x. 
unbiased 
logical. In order for G to be an unbiased estimate of the true population value, calculated gini is multiplied by n/(n1). Default is TRUE. (See Dixon, 1987) 
conf.level 
confidence level for the confidence interval, restricted to lie between 0 and 1.
If set to 
R 
number of bootstrap replicates. Usually this will be a single positive integer.
For importance resampling, some resamples may use one set of weights and others use a different set of weights. In this case R would be a vector of
integers where each component gives the number of resamples from each of the rows of weights. 
type 
character string representing the type of interval required.
The value should be one out of the c( 
na.rm 
logical. Should missing values be removed? Defaults to FALSE. 
The range of the Gini coefficient goes from 0 (no concentration) to √(\frac{n1}{n}) (maximal concentration). The bias corrected Gini coefficient goes from 0 to 1.
The small sample variance properties of the Gini coefficient are not known, and large sample approximations to the variance of the coefficient are poor (Mills and Zandvakili, 1997; Glasser, 1962; Dixon et al., 1987),
therefore confidence intervals are calculated via bootstrap resampling methods (Efron and Tibshirani, 1997).
Two types of bootstrap confidence intervals are commonly used, these are
percentile and biascorrected (Mills and Zandvakili, 1997; Dixon et al., 1987; Efron and Tibshirani, 1997).
The biascorrected intervals are most appropriate for most applications. This is set as default for the type
argument ("bca"
).
Dixon (1987) describes a refinement of the biascorrected method known as 'accelerated' 
this produces values very closed to conventional bias corrected intervals.
(Iain Buchan (2002) Calculating the Gini coefficient of inequality, see: https://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm)
If conf.level
is set to NA
then the result will be

a single numeric value 
and
if a conf.level
is provided, a named numeric vector with 3 elements:
gini 
Gini coefficient 
lwr.ci 
lower bound of the confidence interval 
upr.ci 
upper bound of the confidence interval 
Andri Signorell <andri@signorell.net>
Cowell, F. A. (2000) Measurement of Inequality in Atkinson, A. B. / Bourguignon, F. (Eds): Handbook of Income Distribution. Amsterdam.
Cowell, F. A. (1995) Measuring Inequality Harvester Wheatshef: Prentice Hall.
Marshall, Olkin (1979) Inequalities: Theory of Majorization and Its Applications. New York: Academic Press.
Glasser C. (1962) Variance formulas for the mean difference and coefficient of concentration. Journal of the American Statistical Association 57:648654.
Mills JA, Zandvakili A. (1997). Statistical inference via bootstrapping for measures of inequality. Journal of Applied Econometrics 12:133150.
Dixon, PM, Weiner J., MitchellOlds T, Woodley R. (1987) Bootstrapping the Gini coefficient of inequality. Ecology 68:15481551.
Efron B, Tibshirani R. (1997) Improvements on crossvalidation: The bootstrap method. Journal of the American Statistical Association 92:548560.
See Herfindahl
, Rosenbluth
for concentration measures,
Lc
for the Lorenz curve
ineq()
in the package ineq contains additional inequality measures
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  # generate vector (of incomes)
x < c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)
# compute Gini coefficient
Gini(x)
# working with weights
fl < c(2.5, 7.5, 15, 35, 75, 150) # midpoints of classes
n < c(25, 13, 10, 5, 5, 2) # frequencies
# with confidence intervals
Gini(fl, n, conf.level=0.95, unbiased=FALSE)
# some special cases
x < c(10, 10, 0, 0, 0)
plot(Lc(x))
Gini(x, unbiased=FALSE)
# the same with weights
Gini(x=c(10, 0), n=c(2,3), unbiased=FALSE)
# perfect balance
Gini(c(10, 10, 10))

[1] 0.5134346
gini lwr.ci upr.ci
0.6566810 0.6040134 0.7244841
[1] 0.6
[1] 0.6
[1] 0
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