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Automation and Remote Control

, Volume 80, Issue 6, pp 1058–1068 | Cite as

The Nontransitivity Problem for Three Continuous Random Variables

  • A. V. LebedevEmail author
Stochastic Systems
  • 5 Downloads

Abstract

The nontransitivity problem of the stochastic precedence relation for three independent random variables with distributions from a given class of continuous distributions is studied. Originally, this issue was formulated in one problem of strength theory. In recent time, nontransitivity has become a popular topic of research for the so-called nontransitive dice. Some criteria are first developed and then applied for proving that nontransitivity may not hold for many classical continuous distributions (uniform, exponential, Gaussian, logistic, Laplace, Cauchy, Simpson, one-parameter Weibull and others). The case of all distributions with a polynomial density on the unit interval is considered separately. Some promising directions of further investigations on the subject are outlined.

Keywords

nontransitivity nontransitive dice stochastic precedence continuous distributions 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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