CODEWITHSUNDEEP
rinequalitygini
spsstataR-guy
spsstataR-guy

Reputation: 51

Generalized Gini with Weights in R

I want to calculate weighted generalized gini coefficients. CRAN distributes the "acid" package with a suitable function.

What am i missing here? When weights are constant, the estimates of weighted.gini and sgini are equal given the parameter nu = 2 (as to get the regular gini). When weights are nonconstant, they differ. Is there something fishy going on or am i missing something? They ought to be the same, right?

Checked back with STATA sgini function by van Kerm which is cited in the documentation of acid and its function returns the expected same estimates.

set.seed(123)
install.packages("acid")
library(acid)
x <- rnorm(100,10,1)
w <- rep(1, length(x))
acid::weighted.gini(x,w)$Gini
acid::sgini(x,w,nu=2)$Gini
w <- rnorm(100,10,1)
acid::weighted.gini(x,w)$Gini
acid::sgini(x,w,nu=2)$Gini

Upvotes: 2

Views: 730

Answers (1)

user17481935
user17481935

Reputation: 21

There is a mistake in "sgini". In the formula that the command "sgini" has, at same point, mean(x) is calculated without taking into account the weights.

If we tried to calculate manually the weighted Gini given the formulas: https://core.ac.uk/download/pdf/41339501.pdf

set.seed(123)

x <- rnorm(100,10,1)
w <- rep(1, length(x))
acid::weighted.gini(x,w)$Gini
acid::sgini(x,w,nu=2)$Gini
w <- rnorm(100,10,1)
acid::weighted.gini(x,w)
acid::sgini(x,w,nu=2)

#calc manually
ox<-order(x)
x<-x[ox]
w<-w[ox]
#cov(x,cumsum(x)/cumsum(x)[length(x)])*2/mean(x) #gini without weights
w<-w/sum(w)
f<-w/2+cumsum(c(0,w[-length(w)]))
2/sum(x*w)*sum(w*(x-sum(x*w))*(f-sum(f*w))) #==weighted.gini(x,w)$Gini

Upvotes: 2

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