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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. 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.
    3. 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.
    4. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    5. 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.
    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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