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 \(x_{1},...,x_{n}\).
Entropy coefficient is not well-defined for data vector with zero values whenever parameter is zero or one.
In such case, entropy index coincides with the definition of Theil L index and Theil T index, respectively, and entropy index is calculated with corresponding Theil function.
Theil L always removes zeroes. Theil T enables two ways to deal with zeroes by parameter zeroes.
Option "remove" discard these X's and corresponding weights. Works for power>0.
Option "include" puts \(0\log{0=}0\) due to limiting property of \(p\log{p}\) in zero preserving zero value in dataset. It is valid only for Theil T index, that is power=0.