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Avtomat. i Telemekh., 2019, Issue 6, Pages 91–103 (Mi at15135)  

Stochastic Systems

The nontransitivity problem for three continuous random variables

A. V. Lebedev

Moscow State University, Moscow, Russia

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.

DOI: https://doi.org/10.1134/S0005231019060059

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English version:
Automation and Remote Control, 2019, 80:6, 1058–1068

Bibliographic databases:

Document Type: Article

Received: 05.10.2018
Revised: 18.01.2019
Accepted: 07.02.2019

Citation: A. V. Lebedev, “The nontransitivity problem for three continuous random variables”, Avtomat. i Telemekh., 2019, no. 6, 91–103; Autom. Remote Control, 80:6 (2019), 1058–1068

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