Kolm {wINEQ} | R Documentation |
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")
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.
Value
The value of Kolm coefficient.
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")
[Package wINEQ version 1.2.0 Index]