Atkinson Index - A Measure of Inequality.
The Atkinson index is an inequality measure and is useful in determining which end of the distribution contributed most to the observed inequality.
Atkinson(x, n = rep(1, length(x)), parameter = 0.5, na.rm = FALSE)
x |
a vector containing at least non-negative elements. |
n |
a vector of frequencies, must be same length as x. |
parameter |
parameter of the inequality measure (if set to |
na.rm |
logical. Should missing values be removed? Defaults to FALSE. |
the value of the Akinson Index.
This function was previously published as ineq() in the ineq package and has been
integrated here without logical changes, but with some extensions for NA-handling and the use of weights.
Achim Zeileis <Achim.Zeileis@R-project.org>
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.
See Herfindahl, Rosenbluth for concentration measures and
ineq() in the package ineq for additional inequality measures
# generate vector (of incomes) x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261) # compute Atkinson coefficient with parameter=0.5 Atkinson(x, parameter=0.5)
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