A non-zero dispersion leads to the non-zero bias of mean
A theorem of existence of the non-zero restrictions for the mean of a function on a finite numerical segment at a non-zero dispersion of the function is proved. The theorem has an applied character. It is aimed to be used in the probability theory and statistics and further in economics. Its ultimate aim is to help to answer the Aczél-Luce question whether W(1)=1 and to explain, at least partially, the well-known problems and paradoxes of the utility theory, such as the underweighting of high and the overweighting of low probabilities, the Allais paradox, the four-fold pattern paradox, etc., by purely mathematical methods.
|Date of creation:||11 Jun 2013|
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Web page: https://mpra.ub.uni-muenchen.de
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- Kenneth Y. Chay & Patrick J. McEwan & Miguel Urquiola, 2005.
"The Central Role of Noise in Evaluating Interventions That Use Test Scores to Rank Schools,"
American Economic Review,
American Economic Association, vol. 95(4), pages 1237-1258, September.
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- David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
- Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
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