wINEQ (version 1.2.1)

Jenkins: Jenkins, Cowell and Flachaire

Description

Computes Jenkins as well as Cowell and Flachaire inequality measure of a given variable taking into account weights.

Usage

Jenkins(X, W = rep(1, length(X)), alfa = 0.8)

Value

The value of Jenkins, Cowell and Flachaire coefficient.

Arguments

X

is a data vector

W

is a vector of weights

alfa

is the Jenkins coefficient parameter

Details

Jenkins coefficient is given by: $$J=1-\sum_{j=0}^{K-1} (p_{j+1}-p_{j})(GL_{j}+GL_{j+1})$$

where GL is Generalized Lorenz curve.

Cowell and Flachaire coefficient with alpha parameter is given by: $$I(\alpha)=\frac{1}{\alpha(\alpha-1)}(\frac{1}{N}\sum_{i=1}^{N}s_{i}^{\alpha}-1)$$

for \(\alpha \in (0,1)\), and $$I(0)=-\frac{1}{N}\sum_{i=1}^{N} log(s_{i})$$

for \(\alpha = 0\).

References

Jenkins S. P. and P. J. Lambert: (1997) Three ‘I’s of Poverty Curves, with an Analysis of U.K. Poverty Trends

Cowell F. A.: (2000) Measurement of Inequality, Handbook of Income Distribution

Cowell F. A., Flachaire E.: (2017) Inequality with Ordinal Data

Examples

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

data(Tourism)
#Jenkins, Cowell and Flachaire coefficients for Total expenditure with sample weights
X=Tourism$Total_expenditure
W=Tourism$Sample_weight
Jenkins(X,W)