% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/inequalityMeasure.R
\name{Atkinson}
\alias{Atkinson}
\title{Atkinson index}
\usage{
Atkinson(X, W = rep(1, length(X)), e = 1)
}
\arguments{
\item{X}{is a data vector}

\item{W}{is a vector of weights}

\item{e}{is a coefficient of aversion to inequality, by default 1}
}
\value{
The value of Atkinson coefficient.
}
\description{
Computes Atkinson inequality measure of a given variable taking into account weights.
}
\details{
Atkinson coefficient with respect to parameter \eqn{\epsilon} is given by
\deqn{1-\frac{1}{\mu}{(\frac{1}{n}\sum_{i=1}^{n} x_{i}^{1-\epsilon} )}^{\frac{1}{1-\epsilon}}}
for \eqn{\epsilon \neq 1} and
\deqn{1-\frac{1}{\mu}{(\prod_{i=1}^{n} x_i)}^{\frac{1}{n}}}
for \eqn{\epsilon=1}.
}
\examples{
# Compare weighted and unweighted result
X=1:10
W=1:10
Atkinson(X)
Atkinson(X,W)

data(Tourism)
# Atkinson index for Total expenditure with sample weights
X=Tourism$Total_expenditure
W=Tourism$Sample_weight
Atkinson(X,W)

}
\references{
Atkinson A. B.: (1970) On the measurement of inequality, Journal of Economic Theory
}
