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ineq (version 0.2-13)

# 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 (`NA`s) be removed prior to computations? If set to `FALSE` the computations yield `NA`.

## Value

the value of the inequality measure

## 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.

## 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).

`conc`, `pov`

## Examples

Run this code
``````# 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")
``````

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