polar.wtd {dineq}

Polarization index

Description

Returns the (possibly weighted) polarization index for a vector. The Wolfson index of bipolarization is used.

A bipolarized (income) distribution has fewer observations in the middle and more in lower and/or higher part of the distribution. The regular measures of inequality (like the gini coefficient) does not give information about the polarization of the distribution. This Polarization index computes the level of bipolarization of the distribution. The concept is closely related to the Lorenz curve and therefore the scalar measure is also related to the Gini coefficient. A lower number means a lower level of polarization.

Extension of the polar.aff function in affluence-index package. Option of weighting the index is included.

Usage

polar.wtd(x, weights = NULL)

Arguments

x

a numeric vector.

weights

an optional vector of weights of x to be used in the computation of the Polarization index. Should be NULL or a numeric vector.

Value

The value of the Wolfson polarization index.

Source

Wolny-Dominiak, A. and A. Saczewska-Piotrowska (2017). affluenceIndex: Affluence Indices. R package version 1.0. https://CRAN.R-project.org/package=affluenceIndex

References

Wolfson M. (1994) When inequalities diverge, The American Economic Review, 84, p. 353-358.

Schmidt, A. (2002) Statistical Measurement of Income Polarization. A Cross-National, Berlin 10th International conference on panel data.

Examples

#calculate Polarization Index using Mexican Income data set
data(mex_inc_2008)

#unweighted Polarization Index:
polar.wtd(mex_inc_2008$income)

#weighted Polarization Index:
polar.wtd(x=mex_inc_2008$income, weights=mex_inc_2008$factor)