IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/64646.html
   My bibliography  Save this paper

An existence theorem for restrictions on the mean in the presence of a restriction on the dispersion

Author

Listed:
  • Harin, Alexander

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 non-zero restriction on a central moment |E(X-M)n|≥|rnDisp.n|>0 under the condition 2≤n 0 is the width of a non-zero “forbidden zone” for the mean M near a border of the interval. Here, in the case of , this non-zero restriction is a restriction on the dispersion E(X-M)2≥r2Disp.2=σ2Min>0. So, if there is a non-zero restriction on the dispersion, then a non-zero “forbidden zone” exists for the mean near a border of the interval.

Suggested Citation

  • Harin, Alexander, 2015. "An existence theorem for restrictions on the mean in the presence of a restriction on the dispersion," MPRA Paper 64646, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:64646
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/64646/1/MPRA_paper_64646.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alexander Harin, 2012. "Data Dispersion in Economics(II) - Inevitability and Consequences of Restrictions," Review of Economics & Finance, Better Advances Press, Canada, vol. 2, pages 24-36, November.
    2. Daniel Kahneman & Richard H. Thaler, 2006. "Anomalies: Utility Maximization and Experienced Utility," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 221-234, Winter.
    3. 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.
    4. Alexander Harin, 2010. "The theorem of existence of ruptures in the probability scale," Economics Bulletin, AccessEcon, vol. 30(2), pages 1-16.
    5. Schoemaker, Paul J. H. & Hershey, John C., 1992. "Utility measurement: Signal, noise, and bias," Organizational Behavior and Human Decision Processes, Elsevier, vol. 52(3), pages 397-424, August.
    6. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    7. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harin, Alexander, 2015. "Is Prelec’s function discontinuous at p = 1? (for the Einhorn Award of SJDM)," MPRA Paper 64672, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexander Harin, 2013. "Data dispersion near the boundaries: can it partially explain the problems of decision and utility theories?," Working Papers hal-00851022, HAL.
    2. Harin, Alexander, 2014. "Is data interpretation in utility and prospect theories unquestionably correct?," MPRA Paper 53880, University Library of Munich, Germany.
    3. Harin, Alexander, 2019. "Forbidden zones for the expectations of measurement data and problems of behavioral economics," MPRA Paper 91368, University Library of Munich, Germany.
    4. Harin, Alexander, 2014. "Problems of utility and prospect theories. A discontinuity of Prelec’s function," MPRA Paper 61027, University Library of Munich, Germany.
    5. Harin, Alexander, 2014. "Problems of utility and prospect theories. A ”certain-uncertain” inconsistency of the random-lottery incentive system," MPRA Paper 55706, University Library of Munich, Germany.
    6. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    7. Harin, Alexander, 2014. "Problems of utility and prospect theories. Certainty effect near certainty," MPRA Paper 61026, University Library of Munich, Germany.
    8. Alexander HARIN, 2014. "Partially Unforeseen Events. Corrections and Correcting Formulae for Forecasts," Expert Journal of Economics, Sprint Investify, vol. 2(2), pages 69-79.
    9. Harin, Alexander, 2018. "Forbidden zones and biases for the expectation of a random variable. Version 2," MPRA Paper 85607, University Library of Munich, Germany.
    10. Harin, Alexander, 2015. "An existence theorem for bounds on the expectation of a random variable. Its opportunities for utility theories. V. 2," MPRA Paper 67071, University Library of Munich, Germany.
    11. Harin, Alexander, 2015. "Is Prelec’s function discontinuous at p = 1? (for the Einhorn Award of SJDM)," MPRA Paper 64672, University Library of Munich, Germany.
    12. Harin, Alexander, 2018. "Inequalities and zones. New mathematical results for behavioral and social sciences," MPRA Paper 90326, University Library of Munich, Germany.
    13. Harin, Alexander, 2018. "Forbidden zones for the expectation of a random variable. New version 1," MPRA Paper 84248, University Library of Munich, Germany.
    14. Harin, Alexander, 2015. "An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories," MPRA Paper 66692, University Library of Munich, Germany.
    15. Harin, Alexander, 2011. "Theorem of existence of ruptures for mean values on finite numerical segments. Discrete case," MPRA Paper 35650, University Library of Munich, Germany.
    16. Harin, Alexander, 2023. "To solve old problems of economics. The experimental background," MPRA Paper 117157, University Library of Munich, Germany.
    17. Harin, Alexander, 2015. "Problems of utility and prospect theories. A “certain–uncertain” inconsistency within their experimental methods," MPRA Paper 67911, University Library of Munich, Germany.
    18. Harin, Alexander, 2013. "A non-zero dispersion leads to the non-zero bias of mean," MPRA Paper 47559, University Library of Munich, Germany.
    19. Alexander Harin, 2022. "Forbidden Zones for the Expectations of Data: New Mathematical Methods and Models for Behavioral Economics," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 8(1), pages 12-26, 12-2021.
    20. Harin, Alexander, 2021. "Behavioral economics. Forbidden zones. New method and models," MPRA Paper 106545, University Library of Munich, Germany.

    More about this item

    Keywords

    mean; dispersion; scatter; scattering; noise; probability; economics; utility theory; prospect theory; decision theories; human behavior;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C93 - Mathematical and Quantitative Methods - - Design of Experiments - - - Field Experiments
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:64646. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.