#' Measures of Relative Variability -- Gini Index
#'
#' Gini index for measuring relative inequality (or relative variation) of the data
#' \insertCite{Gini_1912}{lawstat}. \code{NA}s from the data are omitted.
#'
#' @details See also \insertCite{Gastwirth_1988v1;textual}{lawstat}.
#'
#'
#' @param x the input data.
#'
#'
#' @return A list with the following components:
#' \item{statistic}{the Gini index.}
#' \item{parameter}{the mean difference of the set of numbers.}
#' \item{data.name}{a character string giving the name of the data.}
#'
#' @references
#' \insertAllCited{}
#'
#' @seealso \code{\link{cd}}, \code{\link{j.maad}}, \code{\link{lorenz.curve}}
#'
#' @keywords homogeneity variability
#'
#' @author Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth, Weiwen Miao
#'
#' @export
#' @examples
#' ## The Baker v. Carr Case: one-person-one-vote decision.
#' ## Measure of Relative Inequality of Population data in 33 districts
#' ## of the Tennessee Legislature in 1900 and 1972. See
#' ## popdata (see Gastwirth (1988)).
#' data(popdata)
#' gini.index(popdata[,"pop1900"])
#' gini.index(popdata[,"pop1972"])
#'
gini.index <- function(x)
{
DNAME = deparse(substitute(x))
x <- na.omit(x)
x = sort(x)
n = length(x)
### Calculate the delta and Gini Index ###
a <- 0
for (i in 1:(n-1)) {
for (j in (i+1):n) {
a <- a + abs(x[j]- x[i])
}
}
delta <- 2*a/n/(n-1)
GI <- delta/(2*mean(x))
METHOD = "Measures of Relative Variability - Gini Index"
### Display Output ###
STATISTIC = GI
names(STATISTIC) = "Gini Index"
PARAMETER = delta
names(PARAMETER) = "delta"
structure(list(statistic = STATISTIC, parameter = PARAMETER, method = METHOD,
data.name = DNAME),
class = "htest")
}
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