wINEQ (version 1.2.1)

Kolm: Kolm index

Description

Computes Kolm inequality measure of a given variable taking into account weights.

Usage

Kolm(X, W = rep(1, length(X)), parameter = 1, scale = "None")

Value

The value of Kolm coefficient.

Arguments

X

is a data vector

W

is a vector of weights

parameter

is a Kolm parameter

scale

method of data scaling (None, Normalization, Unitarization, Standardization)

Details

Kolm index with parameter \(\alpha\) is defined as: $$K = \frac{1}{ \alpha} (log( \sum_{i=1}^n \exp(\alpha (w_{i} - \mu)) - log(n)))$$

Kolm index is scale-dependent. Basic normalization methods can be applied before final computation.

References

Kolm S. C.: (1976) Unequal inequalities I and II

Kolm S. C.: (1996) Intermediate measures of inequality

Chakravarty S. R.: (2009) Inequality, Polarization and Poverty e-ISBN 978-0-387-79253-8

Examples

# Compare weighted and unweighted result
X=1:10
W=1:10
Kolm(X)
Kolm(X,W)

# Compare raw and standardized data.
Kolm(X,W)
Kolm(X,W, scale ="Standardization")

# Changing units has an impact on the final result
Kolm(X)
Kolm(10*X)

# Changing units has no impact on the final result with standardized data
Kolm(X,scale ="Standardization")
Kolm(10*X,scale ="Standardization")