Entropy {wINEQ}

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 \alpha is equal to Theil_L(X,W) whenever \alpha=0, is equal to Theil_T(X,W) whenever \alpha=1, and whenever \alpha \in (0,1) we have

GE(\alpha) = \frac{1}{\alpha(\alpha-1)W}\sum_{i=1}^{n}w_{i}\left(\left(\frac{x_{i}}{\mu}\right)^\alpha-1\right)

where W is a sum of weights and \mu is the arithmetic mean of x_{1},...,x_{n}.

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)