Irina Gennad'EVna Shevtsova

Current Organizations / Institutes

The organizations/institutes from the scholar's latest article

Lomonosov Moscow State University

Previous Organizations / Institutes

The organizations / institutes from the scholar's other articles in the past ten years

Research Subjects

Research Interests

Irina Gennad'EVna Shevtsova has a total of 21 co-authors. Here are the top co-authors by number of shared publications:

Viktor Yur'EVich Korolev
Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia
9 shared publications
Vladimir Makarenko
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, 1/52, 119991 Moscow, Russia
4 shared publications
Mikhail Tselishchev
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
3 shared publications
R. A. Gabdullin
Moscow State University
3 shared publications
V.A. Makarenko
Moscow State University
3 shared publications
Lutz Mattner
Universität Trier, Fachbereich IV – Mathematik, 54286 Trier, Germany
2 shared publications

Latest Publications

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- 26 July 2026
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
On the Moments of the Kolmogorov and Logistic Distributions
by V. Yu. Korolev, I. G. Shevtsova
We find moments of the Kolmogorov distribution of all real orders in terms of Riemann’s zeta and Euler’s gamma functions. As a corollary, using
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- 26 July 2026
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
On the Moments of the Kolmogorov and Logistic Distributions
by V. Yu. Korolev, I. G. Shevtsova
We find moments of the Kolmogorov distribution of all real orders in terms of Riemann’s zeta and Euler’s gamma functions. As a corollary, using
Website
Google Scholar
- 26 July 2026
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
On the Inifite Divisibility of Nonnegative Integer-Valued Random Variables
by I. G. Shevtsova
We prove that a nonnegative integer-valued infinitely divisible random variable is infinitely divisible in the class of nonnegative integer-valued random v
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- 26 July 2026
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
On the Inifite Divisibility of Nonnegative Integer-Valued Random Variables
by I. G. Shevtsova
We prove that a nonnegative integer-valued infinitely divisible random variable is infinitely divisible in the class of nonnegative integer-valued random v
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- 14 November 2025
- Published by Springer Nature in Sankhya A
Editorial: Special Issues in Sankhya A and Sankhya B in Memory of Prof. C. Radhakrishna Rao (1920-2023)
by Ravindra Khattree, Irina Shevtsova, Anuradha Roy, Arni S. R. Srinivasa Rao
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- 14 November 2025
- Published by Springer Nature in Sankhya A
Editorial: Special Issues in Sankhya A and Sankhya B in Memory of Prof. C. Radhakrishna Rao (1920-2023)
by Ravindra Khattree, Irina Shevtsova, Anuradha Roy, Arni S. R. Srinivasa Rao
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- 23 October 2025
- Published by Springer Nature in Sankhya A
Discussion of D. Kundu’s Article in Sankhya A: Bayesian Inference of a Stationary Proportional Hazard Class Process
by Irina Shevtsova
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- 23 October 2025
- Published by Springer Nature in Sankhya A
Discussion of D. Kundu’s Article in Sankhya A: Bayesian Inference of a Stationary Proportional Hazard Class Process
by Irina Shevtsova
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- 9 October 2025
- Published by Springer Nature in Sankhya A
Discussion of A. Bulinski and Sh. Wang’s Article in Sankhya A: Statistical Estimation of Conditional Interaction Information by Delta Method
by Irina Shevtsova
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- 9 October 2025
- Published by Springer Nature in Sankhya A
Discussion of A. Bulinski and Sh. Wang’s Article in Sankhya A: Statistical Estimation of Conditional Interaction Information by Delta Method
by Irina Shevtsova
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Cited by 3
- 1 December 2024
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
Asymptotic and Analytic Properties of Mixture Probability Models and Their Application to the Analysis of Complex Systems
by V. Yu. Korolev, I. G. Shevtsova, O. V. Shestakov
The paper presents a survey of the results obtained by the members of the Department of Mathematical Statistics in the field of analytic and asymptotic pro
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- 1 December 2024
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
Asymptotic and Analytic Properties of Mixture Probability Models and Their Application to the Analysis of Complex Systems
by V. Yu. Korolev, I. G. Shevtsova, O. V. Shestakov
The paper presents a survey of the results obtained by the members of the Department of Mathematical Statistics in the field of analytic and asymptotic pro
Cited by 3
Open Access
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Cited by 1
- 26 January 2023
- Published by MDPI AG in Mathematics
Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions
by Vladimir Makarenko, Irina Shevtsova
For each $t \in (- 1, 1)$ , the exact value of the least upper bound $H (t) = sup {E | X |^{3} / E | X - t |^{3}}$ over all the non-degenerate distributions of the random variable X with a fixed normalized first-order moment $E X_{1} / \sqrt{E X_{1}^{2}} = t$ , and a finite third-order moment is obtained, yielding the exact value of the unconditional supremum $M : = sup L_{1} (X) / L_{1} (X - E X) = (\sqrt{17 + 7 \sqrt{7}}) / 4$ , where $L_{1} (X) = E {| X |}^{3} / {(E X^{2})}^{3 / 2}$ is the non-central Lyapunov ratio, and hence proving S. Shorgin’s (2001) conjecture on the exact value of M. As a corollary, an analog of the Berry–Esseen inequality for the Poisson random sums of independent identically distributed random variables $X_{1}, X_{2}, \dots$ is proven in terms of the central Lyapunov ratio $L_{1} (X_{1} - E X_{1})$ with the constant $0.3031 \cdot H (t) {(1 - t^{2})}^{3 / 2} \in [0.3031, 0.4517)$ , $t \in [0, 1)$ , which depends on the normalized first-moment $t : = E X_{1} / \sqrt{E X_{1}^{2}}$ of random summands and being arbitrarily close to $0.3031$ for small values of t, an almost $1.5$ size improvement from the previously known one.
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- 26 January 2023
- Published by MDPI AG in Mathematics
Open Access
Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions
by Vladimir Makarenko, Irina Shevtsova
For each $t \in (- 1, 1)$ , the exact value of the least upper bound $H (t) = sup {E | X |^{3} / E | X - t |^{3}}$ over all the non-degenerate distributions of the random variable X with a fixed normalized first-order moment $E X_{1} / \sqrt{E X_{1}^{2}} = t$ , and a finite third-order moment is obtained, yielding the exact value of the unconditional supremum $M : = sup L_{1} (X) / L_{1} (X - E X) = (\sqrt{17 + 7 \sqrt{7}}) / 4$ , where $L_{1} (X) = E {| X |}^{3} / {(E X^{2})}^{3 / 2}$ is the non-central Lyapunov ratio, and hence proving S. Shorgin’s (2001) conjecture on the exact value of M. As a corollary, an analog of the Berry–Esseen inequality for the Poisson random sums of independent identically distributed random variables $X_{1}, X_{2}, \dots$ is proven in terms of the central Lyapunov ratio $L_{1} (X_{1} - E X_{1})$ with the constant $0.3031 \cdot H (t) {(1 - t^{2})}^{3 / 2} \in [0.3031, 0.4517)$ , $t \in [0, 1)$ , which depends on the normalized first-moment $t : = E X_{1} / \sqrt{E X_{1}^{2}}$ of random summands and being arbitrarily close to $0.3031$ for small values of t, an almost $1.5$ size improvement from the previously known one.
Cited by 1
Open Access
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- 26 December 2022
- Published by MDPI AG in Preprints.org
Delicate Comparison of the Central and Non-central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions
by Vladimir Makarenko, Irina Shevtsova
For each $t\in(-1,1)$, exact values of the least upper bounds $$ H(t)=\sup_{\E X=t,\,\E X^2=1} \frac{\E\abs{X}^3}{\E \abs{X-t}^3},\quad \sup_{\E X=t,\,\E X^2=1} \frac{L_1(X)}{L_1(X-t)} $$ are obtained, where $L_1(X)=\E|X|^3/(\E X^2)^{3/2}$ is the non-cental Lyapunov ratio. It is demonstrated that these values are attained only at two-point distributions. As a corollary, S.\,Shorgin's conjecture is proved that states that the exact value is $$ \sup\frac{L_1(X)}{L_1(X-\E X)}= \frac{\sqrt{17 + 7\sqrt7}}{4} = 1.4899\ldots, $$ where the supremum is taken over all non-degenerate distributions of the random variable $X$ with the finite third moment. Also, in terms of the central Lyapunov ratio $L_1(X-\E X)$, an analog of the Berry--Esseen inequality is proved for Poisson random sums of independent identically distributed random variables with the constant $$ 0.3031\cdot H\left(\frac{\E X}{\sqrt{\E X^2}}\right) \left(1-\frac{(\E X)^2}{\E X^2}\right)^{3/2} \le 0.3031\cdot \frac{\sqrt{17 + 7\sqrt7}}{4}<0.4517.$$ where $\Law(X)$ is the common distribution of the summands.
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- 26 December 2022
- Published by MDPI AG in Preprints.org
Open Access
Delicate Comparison of the Central and Non-central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions
by Vladimir Makarenko, Irina Shevtsova
For each $t\in(-1,1)$, exact values of the least upper bounds $$ H(t)=\sup_{\E X=t,\,\E X^2=1} \frac{\E\abs{X}^3}{\E \abs{X-t}^3},\quad \sup_{\E X=t,\,\E X^2=1} \frac{L_1(X)}{L_1(X-t)} $$ are obtained, where $L_1(X)=\E|X|^3/(\E X^2)^{3/2}$ is the non-cental Lyapunov ratio. It is demonstrated that these values are attained only at two-point distributions. As a corollary, S.\,Shorgin's conjecture is proved that states that the exact value is $$ \sup\frac{L_1(X)}{L_1(X-\E X)}= \frac{\sqrt{17 + 7\sqrt7}}{4} = 1.4899\ldots, $$ where the supremum is taken over all non-degenerate distributions of the random variable $X$ with the finite third moment. Also, in terms of the central Lyapunov ratio $L_1(X-\E X)$, an analog of the Berry--Esseen inequality is proved for Poisson random sums of independent identically distributed random variables with the constant $$ 0.3031\cdot H\left(\frac{\E X}{\sqrt{\E X^2}}\right) \left(1-\frac{(\E X)^2}{\E X^2}\right)^{3/2} \le 0.3031\cdot \frac{\sqrt{17 + 7\sqrt7}}{4}<0.4517.$$ where $\Law(X)$ is the common distribution of the summands.
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- 1 December 2022
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
Improving Constants in Esseen–Rozovskii Type Inequalities for Identically Distributed Random terms
by A. V. Maksimova, I. G. Shevtsova
Constants in Esseen–Rozovskii type inequalities proposed by Gabdullin, Makarenko, and Shevtsova (2018) are improved for one of the most important spe
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- 1 December 2022
- Published by Allerton Press in Moscow University Computational Mathematics and Cybernetics
Improving Constants in Esseen–Rozovskii Type Inequalities for Identically Distributed Random terms
by A. V. Maksimova, I. G. Shevtsova
Constants in Esseen–Rozovskii type inequalities proposed by Gabdullin, Makarenko, and Shevtsova (2018) are improved for one of the most important spe
Open Access
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Cited by 4
- 4 July 2021
- Published by MDPI AG in Mathematics
On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums
by Irina Shevtsova, Mikhail Tselishchev
We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.
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- 4 July 2021
- Published by MDPI AG in Mathematics
Open Access
On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums
by Irina Shevtsova, Mikhail Tselishchev
We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.
Cited by 4

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