# TheilU: Theil's U Index of Inequality In DescTools: Tools for Descriptive Statistics

## Description

Calculate Theil's U index of inequality.

## Usage

 `1` ```TheilU(a, p, type = c(2, 1), na.rm = FALSE) ```

## Arguments

 `a` a numeric vector with the actual observed values. `p` a numeric vector containing the predictions. `type` defining the type of Theil's two U measures, see Details. Default is 2. `na.rm` logical, indicating whether `NA` values should be stripped before the computation proceeds. If set to `TRUE` complete cases of `cbind(x, y)` will be used. Defaults to `FALSE`.

## Details

Theil proposed two error measures, but at different times and under the same symbol U, which has caused some confusion. U `type = 1` is taken from Theil (1958, pp. 31-42). The argument `a` represents the actual observations and `p` the corresponding predictions. He left it open whether `a` and `p` should be used as absolute values or as observed and predicted changes.
Theil (1966, chapter 2) proposed U `type = 2` as a measure of forecast quality: "...where A_i and P_i stand for a pair of predicted and observed changes. ..."
As U_1 has some serious disadvantages (see Bliemel 1973) it is recommended to use U_2.

## Author(s)

Andri Signorell <andri@signorell.net>

## References

Theil, H. (1958): Economic Forecasts and Policy. Amsterdam: North Holland.

Thiel, H. (1966): Applied Economic Forecasting. Chicago: Rand McNally.

Bliemel, F. (1973): Theil's Forecast Accuracy Coefficient: A Clarification, Journal of Marketing Research Vol. 10, No. 4 (Nov., 1973), pp. 444-446

`Gini`

## Examples

 ```1 2``` ```TheilU(1:10, 2:11, type=1) TheilU(1:10, 2:11, type=2) ```

### Example output

```[1] 0.07512486
[1] 0.1611646
```

DescTools documentation built on June 17, 2021, 5:12 p.m.