wINEQ (version 1.2.1)

RicciSchutz: Ricci and Schutz index

Description

Computes Ricci and Schutz inequality measure of a given variable taking into account weights.

Usage

RicciSchutz(X, W = rep(1, length(X)))

Value

The value of Ricci and Schutz coefficient.

Arguments

X

is a data vector

W

is a vector of weights

Details

In the case of an empirical distribution with n elements where \(y_{i}\) denotes the wealth of household \(i\) and \(\overline{y}\) the sample average, the Ricci and Schutz coefficient can be expressed as: $$RS = \frac{1}{2n} \sum_{i=1}^{n} \frac{\mid y_{i} - \overline{y} \mid}{\overline{y}}$$

References

Coulter P. B.: (1989) Measuring Inequality ISBN 0-8133-7726-9

Eliazar I. I., Sokolov I. M.: (2010) Measuring statistical heterogeneity: The Pietra index

Costa R. N., Pérez-Duarte S.: (2019) Not all inequality measures were created equal, Statistics Paper Series, No 31

Examples

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

data(Tourism)
#Ricci and Schutz index for Total expenditure with sample weights
X=Tourism$Total_expenditure
W=Tourism$Sample_weight
RicciSchutz(X,W)