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This article is cited in 1 scientific paper (total in 1 paper)
Nontransitive triplets of continuous random variables and their applications
A. V. Lebedev Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Main Building, 1 Leninskiye
Gory, Moscow 119991, Russian Federation
Abstract:
The phenomenon of nontransitivity of the stochastic precedence relation
for three independent random variables with distributions from some classes
of continuous distributions is studied. Initially, this question was posed
in connection with the application in strength theory. With paired comparisons
of iron bars from three factories, a paradoxical situation may arise when
the bars from the first factory are “worse” than the bars from the second
factory, the bars from the second factory are “worse” than the bars from the
third factory, and the bars from the third factory are “worse”
than the bars from the first factory. Further, the nontransitivity topic gained
popularity for the example of the so-called nontransitive dice; however, this
led to its narrowing down to discrete random variables with finite sets of
values. The paper presents that for mixtures of normal and exponential
distributions, nontransitivity is possible in a wide range of parameters.
Specific features of the mutual arrangement of the graphs of the distribution
functions in these cases are indicated.
Keywords:
nontransitivity, nontransitive dice, stochastic precedence, continuous distributions, mixtures of distributions.
Received: 03.10.2018
Citation:
A. V. Lebedev, “Nontransitive triplets of continuous random variables and their applications”, Inform. Primen., 13:3 (2019), 20–26
Linking options:
https://www.mathnet.ru/eng/ia605 https://www.mathnet.ru/eng/ia/v13/i3/p20
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Abstract page: | 227 | Full-text PDF : | 81 | References: | 16 |
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