ineq {ineq}

Inequality Measures

Description

computes the inequality within a vector according to the specified inequality measure

Usage

ineq(x, parameter = NULL, type = c("Gini", "RS", "Atkinson", "Theil", "Kolm", "var",
     "square.var", "entropy"), na.rm = TRUE)

Gini(x, corr = FALSE, na.rm = TRUE)
RS(x, na.rm = TRUE)
Atkinson(x, parameter = 0.5, na.rm = TRUE)
Theil(x, parameter = 0, na.rm = TRUE)
Kolm(x, parameter = 1, na.rm = TRUE)
var.coeff(x, square = FALSE, na.rm = TRUE)
entropy(x, parameter = 0.5, na.rm = TRUE)

Arguments

x

a vector containing at least non-negative elements

parameter

parameter of the inequality measure (if set to NULL the default parameter of the respective measure is used)

type

character string giving the measure used to compute inequality. must be one of the strings in the default argument (the first character is sufficient). defaults to "Gini".

corr

logical. Argument of the function Gini specifying whether or not a finite sample correction should be applied.

square

logical. Argument of the function var.coeff, for details see below.

na.rm

logical. Should missing values (NAs) be removed prior to computations? If set to FALSE the computations yield NA.

Details

ineq is just a wrapper for the inequality measures Gini, RS, Atkinson, Theil, Kolm,var.coeff, entropy. If parameter is set to NULL the default from the respective function is used.

Gini is the Gini coefficient, RS is the the Ricci-Schutz coefficient (also called Pietra's measure), Atkinson gives Atkinson's measure and Kolm computes Kolm's measure.

If the parameter in Theil is 0 Theil's entropy measure is computed, for every other value Theil's second measure is computed.

ineq(x, type="var") and var.coeff(x) respectively compute the coefficient of variation, while ineq(x,type="square.var") and var.coeff(x, square=TRUE) compute the squared coefficient of variation.

entropy computes the generalized entropy, which is for parameter 1 equal to Theil's entropy coefficient and for parameter 0 equal to the second measure of Theil.

Value

the value of the inequality measure

References

F A Cowell: Measurement of Inequality, 2000, in A B Atkinson / F Bourguignon (Eds): Handbook of Income Distribution, Amsterdam,

F A Cowell: Measuring Inequality, 1995 Prentice Hall/Harvester Wheatshef,

Marshall / Olkin: Inequalities: Theory of Majorization and Its Applications, New York 1979 (Academic Press).

See Also

conc, pov

Examples

# generate vector (of incomes)
x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)
# compute Gini coefficient
ineq(x)
# compute Atkinson coefficient with parameter=0.5
ineq(x, parameter=0.5, type="Atkinson")