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Auto-Transformations of the Probability Density Functions

Author

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  • Alexander Harin

    (Modern University for the Humanities, Moscow, Russia)

Abstract

The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions (PDFs) of random variables into some similar functions having smaller sizes of their domains. 2) To research and outline basic features of these auto-transformations of PDFs. Particularly, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences.

Suggested Citation

  • Alexander Harin, 2021. "Auto-Transformations of the Probability Density Functions," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(3), pages 167-178, 07-2021.
    • Handle: RePEc:arp:ajoams:2021:p:167-178
    DOI: 10.32861/ajams.73.167.178
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    References listed on IDEAS

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    1. Scheutzow, Michael, 1985. "Noise can create periodic behavior and stabilize nonlinear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 323-331, September.
    2. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    3. R. Sharma & R. Bhandari, 2014. "On Variance Upper Bounds for Unimodal Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(21), pages 4503-4513, November.
    4. 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.
    5. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    6. Harin, Alexander, 2018. "Inequalities and zones. New mathematical results for behavioral and social sciences," MPRA Paper 90326, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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