Entropy {wINEQ} | R Documentation |
Generalized entropy index
Description
Computes generalized entropy index of a given variable taking into account weights.
Usage
Entropy(X, W = rep(1, length(X)), parameter = 0.5)
Arguments
X |
is a data vector |
W |
is a vector of weights |
parameter |
is a entropy parameter |
Details
Entropy coefficient with respect to parameter is equal to Theil_L(X,W) whenever
,
is equal to Theil_T(X,W) whenever
, and whenever
we have
where is a sum of weights and
is the arithmetic mean of
.
Value
The value of generalized entropy index
References
Shorrocks A. F.: (1980) The Class of Additively Decomposable Inequality Measures. Econometrica
Pielou E.C.: (1966) The measurement of diversity in different types of biological collections. Journal of Theoretical Biology
Examples
# Compare weighted and unweighted result
X=1:10
W=1:10
Entropy(X)
Entropy(X,W)
data(Tourism)
# Generalized entropy index for Total expenditure with sample weights
X=Tourism$`Total expenditure`
W=Tourism$`Sample weight`
Entropy(X,W)
[Package wINEQ version 1.2.0 Index]