Theil_T {wINEQ} | R Documentation |
Theil T
Description
Computes Theil_T
inequality measure of a given variable taking into account weights.
Usage
Theil_T(X, W = rep(1, length(X)), zeroes = "include")
Arguments
X |
is a data vector |
W |
is a vector of weights |
zeroes |
defines what to do with zeroes in the data vector. Possible options are "remove" and "include". See Details for more. |
Details
Theil T index is defined as:
T_{T} = T_{\alpha=1} = \frac{1}{N} \sum_{i=1}^N \frac{ x_{i} }{\mu} ln \big( \frac{ x_{i} }{\mu} \big)
where
\mu = \frac{1}{N} \sum_{i=1}^N x_{i}
Formally, Theil index is defined for positive values due to logarithms.
Nevertheless, in data analysis zero values may occur.
There are two way we can deal with them.
Option "remove" discard these X's and corresponding weights.
Option "include" puts 0\log{0=}0
due to limiting property of p\log{p}
in zero preserving zero value in dataset.
Value
The value of Theil_T
coefficient.
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_T(X)
Theil_T(X,W)
data(Tourism)
# Theil T coefficient for Total expenditure with sample weights
X=Tourism$Total_expenditure
W=Tourism$Sample_weight
Theil_T(X,W)