Avtomat. i Telemekh., 2019, Issue 6, Pages 91–103
The nontransitivity problem for three continuous random variables
A. V. Lebedev
Moscow State University, Moscow, Russia
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.
nontransitivity, nontransitive dice, stochastic precedence, continuous distributions.
PDF file (824 kB)
First page: PDF file
Automation and Remote Control, 2019, 80:6, 1058–1068
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
Citation in format AMSBIB
\paper The nontransitivity problem for three continuous random variables
\jour Avtomat. i Telemekh.
\jour Autom. Remote Control
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|