Theil's U Index of Inequality
Calculate Theil's U index of inequality.
TheilU(a, p, type = c(2, 1), na.rm = FALSE)
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 |
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.
Andri Signorell <andri@signorell.net>
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
TheilU(1:10, 2:11, type=1) TheilU(1:10, 2:11, type=2)
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