Leti {wINEQ}

Leti index

Description

Computes Leti inequality measure of a given variable taking into account weights.

Usage

Leti(X, W = rep(1, length(X)), norm = T)

Arguments

X

is a data vector (ordered factor or numeric)

W

is a vector of weights

norm

(logical). If TRUE (default) then Leti index is divided by a maximum possible value which is (k-1)/2 where k in a number of categories.

Details

Let n_{i} be the number of individuals in category i and let N be the total sample size. Cumulative distribution is given by F_{i} = \frac{\sum_{j=1}^{i} n_{j}}{N}. Leti index is defined as:

L =2 \sum_{i=1}^{k-1} F_{i}(1-F_{i})

Value

The value of Leti coefficient.

References

Leti G.: (1983). Statistica descrittiva, il Mulino, Bologna. ISBN: 8-8150-0278-2

Examples

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

data(Tourism)
#Leti index for Total expenditure with sample weights
X=Tourism$`Total expenditure`
W=Tourism$`Sample weight`
Leti(X,W)