wINEQ (version 1.2.1)

Theil_L: Theil L

Description

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

Usage

Theil_L(X, W = rep(1, length(X)))

Value

The value of Theil_L coefficient.

Arguments

X

is a data vector

W

is a vector of weights

Details

Theil L index is defined as: $$T_{L} = T_{\alpha=0} = \frac{1}{N} \sum_{i=1}^N ln \big(\frac{\mu }{x_{i}} \big)$$ where $$\mu = \frac{1}{N} \sum_{i=1}^N x_{i}$$ Theil L index can be computed only for positive values. By default, this functions discard zero X's and corresponding weights.

References

Serebrenik A., van den Brand M.: Theil index for aggregation of software metrics values. 26th IEEE International Conference on Software Maintenance. IEEE Computer Society.

Conceição P., Ferreira P.: (2000) The Young Person’s Guide to the Theil Index: Suggesting Intuitive Interpretations and Exploring Analytical Applications

OECD: (2020) Regions and Cities at a Glance 2020, Chapter: Indexes and estimation techniques

Examples

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

data(Tourism)
# Theil L coefficient for Total expenditure with sample weights
X=Tourism$Total_expenditure
W=Tourism$Sample_weight
Theil_L(X,W)