Modeling the Evolution of the Sample Distributions of Random Variables Using the Liouville Equation

We consider the difference approximation of the one-dimensional Liouville equation for modeling the evolution of the sample distribution density (of the nonstationary time series) estimated by a histogram. It is shown that the change in the sample density of the distribution over a certain period of...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2020-09, Vol.12 (5), p.747-756
Main Authors: Kislitsin, A. A., Orlov, Yu. N.
Format: Article
Language:English
Subjects:
Algorithms
Density distribution
Distribution functions
Evolution
Histograms
Liouville equations
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Modelling
Random variables
Simulation and Modeling
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Summary:We consider the difference approximation of the one-dimensional Liouville equation for modeling the evolution of the sample distribution density (of the nonstationary time series) estimated by a histogram. It is shown that the change in the sample density of the distribution over a certain period of time can be numerically described as a solution of the Liouville equation if the initial density distribution is strictly positive in the internal class intervals. The algorithm for determining the corresponding rate is constructed and its mechanical and statistical meaning is shown as a semigroup equivalent in the Chernoff sense to the average semigroup, which generates the evolution of the distribution function.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048220050087