Harin, Alexander (2015): An existence theorem for restrictions on the mean in the presence of a restriction on the dispersion.

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Abstract
This article analyzes, from the purely mathematical point of view, a general practical problem. The problem consists in the influence of the scatter of experimental data on their mean values (and, possibly, on the probability) near the borders of intervals. The second central moment, the dispersion is a common measure of a scatter. Suppose, for instance, a nonnegative random variable X takes values in a finite interval . Write M for its mean. If there is a nonzero restriction on a central moment E(XM)n≥rnDisp.n>0 under the condition 2≤n<∞, then A<(A+rnDisp.n/(BA)n)≤M≤(BrnDisp.n/(BA)n). That is, rnDisp.n/(BA)n)>0 is the width of a nonzero “forbidden zone” for the mean M near a border of the interval. Here, in the case of , this nonzero restriction is a restriction on the dispersion E(XM)2≥r2Disp.2=σ2Min>0. So, if there is a nonzero restriction on the dispersion, then a nonzero “forbidden zone” exists for the mean near a border of the interval.
Item Type:  MPRA Paper 

Original Title:  An existence theorem for restrictions on the mean in the presence of a restriction on the dispersion 
Language:  English 
Keywords:  mean; dispersion; scatter; scattering; noise; probability; economics; utility theory; prospect theory; decision theories; human behavior; 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C9  Design of Experiments > C91  Laboratory, Individual Behavior C  Mathematical and Quantitative Methods > C9  Design of Experiments > C93  Field Experiments D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  64646 
Depositing User:  Alexander Harin 
Date Deposited:  27. May 2015 20:56 
Last Modified:  27. May 2015 21:52 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/64646 