# TheilU

0th

Percentile

##### Theil's U Index of Inequality

Calculate Theil's U index of inequality.

Keywords
multivar
##### Usage
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 $U_2$.

##### 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

• TheilU
##### Examples
TheilU(1:10, 2:11, type=1)
TheilU(1:10, 2:11, type=2)

Documentation reproduced from package DescTools, version 0.99.19, License: GPL (>= 2)

### Community examples

navid.nobani@gmail.com at Oct 27, 2017 DescTools v0.99.19

library(forecast) a <- c(1,2,3,5,6,8,9) #actual p <- c(1,3,3,4,6,7,9) #forecasted TheilU(a,p)  [1] 0.1167748