Results 1 to 10 of about 440,741 (146)

Comparing Distributions of Sums of Random Variables by Deficiency: Discrete Case

Mathematics, 2022
In the paper, we consider a new approach to the comparison of the distributions of sums of random variables. Unlike preceding works, for this purpose we use the notion of deficiency that is well known in mathematical statistics.
Vladimir E. Bening, Victor Y. Korolev
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A Rényi-Type Limit Theorem on Random Sums and the Accuracy of Likelihood-Based Classification of Random Sequences with Application to Genomics

Mathematics, 2023
We study classification of random sequences of characters selected from a given alphabet into two classes characterized by distinct character selection probabilities and length distributions.
Leonid Hanin, Lyudmila Pavlova
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Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization

Mathematics, 2023
In the paper, quasi-exponentiated normal distributions are introduced for any real power (exponent) no less than two. With natural exponents, the quasi-exponentiated normal distributions coincide with the distributions of the corresponding powers of ...
Victor Korolev, Alexander Zeifman
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Modeling Particle Size Distribution in Lunar Regolith via a Central Limit Theorem for Random Sums

Mathematics, 2020
A version of the central limit theorem is proved for sums with a random number of independent and not necessarily identically distributed random variables in the double array limit scheme.
Andrey Gorshenin, Victor Korolev, Alexander Zeifman   +2 more
doaj   +1 more source

Angle Sums of Random Polytopes

Michigan Mathematical Journal, 2023
23 pages, no figures. Compared to the previous version, new results in Section 4.4 and their proofs have been added.
Godland, Thomas, Kabluchko, Zakhar, Zaporozhets, Dmitry   +2 more
openaire   +2 more sources

Some Properties of Univariate and Multivariate Exponential Power Distributions and Related Topics

Mathematics, 2020
In the paper, a survey of the main results concerning univariate and multivariate exponential power (EP) distributions is given, with main attention paid to mixture representations of these laws.
Victor Korolev
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Convergence in Total Variation of Random Sums

Mathematics, 2021
Let (Xn) be a sequence of real random variables, (Tn) a sequence of random indices, and (τn) a sequence of constants such that τn→∞. The asymptotic behavior of Ln=(1/τn)∑i=1TnXi, as n→∞, is investigated when (Xn) is exchangeable and independent of (Tn ...
Luca Pratelli, Pietro Rigo
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Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions

Mathematics, 2023
Analytic and asymptotic properties of the generalized Student and generalized Lomax distributions are discussed, with the main focus on the representation of these distributions as scale mixtures of the laws that appear as limit distributions in ...
Victor Korolev
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Discrepancy for randomized Riemann sums [PDF]

Proceedings of the American Mathematical Society, 2009
Let \(N\in\mathbb N\) be a given large number, and \(V_N= \{v_1,\dots, v_N\}\) be a distribution of \(N\) points in the unit cube \([-1/2,1/2)^d\), treated as the torus \(\mathbb{T}^d\). Let \(d\mu\) denote a probability measure on \(\mathbb{T}^d\). For every \(j= 1,\dots,N\), let \(d\mu_j\) denote the measure obtained after translating \(d\mu\) by ...
BRANDOLINI, Luca, CHEN, WILLIAM W. L., GIGANTE, Giacomo, TRAVAGLINI, GIANCARLO   +3 more
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Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems

Mathematics, 2020
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced.
Yury Khokhlov, Victor Korolev, Alexander Zeifman   +2 more
doaj   +1 more source