Gini(x, n = rep(1, length(x)), unbiased = TRUE, conf.level = NA, R = 1000, type = "bca", na.rm = FALSE)
NA, if x contains negative elements.
TRUEthe bootstrap confidence intervals are calculated. If set to
NA(default) no confidence intervals are returned.
"bca"). This argument is ignored if no confidence intervals are to be calculated.
conf.levelis set to
NAthen the result will be then the result will be and if a
conf.levelis provided, a named numeric vector with 3 elements:
"bca"). Dixon (1987) describes a refinement of the bias-corrected method known as 'accelerated' - this produces values very closed to conventional bias corrected intervals. (Iain Buchan (2002) Calculating the Gini coefficient of inequality, see: http://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm)
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 57:648-654.
Mills JA, Zandvakili A. (1997). Statistical inference via bootstrapping for measures of inequality. Journal of Applied Econometrics 12:133-150.
Dixon, PM, Weiner J., Mitchell-Olds T, Woodley R. (1987) Boot-strapping the Gini coefficient of inequality. Ecology 68:1548-1551.
Efron B, Tibshirani R. (1997) Improvements on cross-validation: The bootstrap method. Journal of the American Statistical Association 92:548-560.
Rosenbluthfor concentration measures,
Lcfor the Lorenz curve
ineq()in the package ineq contains additional inequality measures
# 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))
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