SciencesPo (version 1.4.0)

Atkinson: Atkinson Index of Inequality

Description

Calculates the Atkinson index A. This inequality measure is especially good at determining which end of the distribution is contributing most to the observed inequality.

Usage

Atkinson(x, n = rep(1, length(x)), epsilon = NULL, na.rm = FALSE, ...)
"Atkinson"(x, n = rep(1, length(x)), epsilon = NULL, na.rm = FALSE, ...)

Arguments

x

a vector of data values of non-negative elements.

n

a vector of frequencies of the same length as x.

epsilon

a parameter of the inequality measure (if NULL, the default parameter (0.5) of the respective measure is used).

na.rm

logical. Should missing values be removed? Defaults is set to FALSE.

...

additional arguements (currently ignored)

Details

epsilon = 0,5: little inequality aversion epsilon = 1,0: medium inequality aversion epsilon = 2,0: great inequality aversion

References

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.

See Also

Herfindahl, Rosenbluth, Gini. For more details see the “Indices” vignette.

Examples

if (interactive()) {
# generate a vector (of incomes)
# y <- c(80, 60, 10, 20, 30)
# Entropy 1.392321
# Maximum Entropy	1.609438
# Normalized Entropy	0.865098
# Exponential Index	0.248498
# Herfindahl	0.285000
# Normalized Herfindahl	0.106250
# Gini Coefficient	0.360000
# Concentration Coefficient	0.450000

x <- c(778, 815, 857, 888, 925, 930, 965, 990, 1012)

# compute Atkinson coefficient with epsilon=0.5
Atkinson(x, epsilon=0.5)

w <- c(10, 15, 20, 25, 40, 20, 30, 35, 45, 90)
}