TheilU
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 toTRUE
complete cases ofcbind(x, y)
will be used. Defaults toFALSE
.
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. 3142). 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. 444446
See Also
Examples
TheilU(1:10, 2:11, type=1)
TheilU(1:10, 2:11, type=2)
Community examples
```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