A non-zero dispersion leads to the non-zero bias of mean

Harin, Alexander (2013): A non-zero dispersion leads to the non-zero bias of mean.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: utility; utility theory; probability; uncertainty; decisions; economics; Prelec; probability weighting; Allais paradox; risk aversion
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; G - Financial Economics > G2 - Financial Institutions and Services > G22 - Insurance ; Insurance Companies ; Actuarial Studies

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