Absolutely Continuous, Log-Concave Unimodal Distributions

Authors

  • Yuri P. Virchenko Belgorod State Technological University named after V. G. Shukhov
  • Amanuel M. Tewolde Belgorod National Research University

DOI:

https://doi.org/10.52575/2687-0959-2025-57-3-208-223

Keywords:

Convex Functions, Composition of Distributions, Univariate Probability Distributions, Unimodal Distributions, Strong Unimodality

Abstract

In this paper, we study strongly unimodal distribution functions on R according to I. A. Ibragimov. We improve the proof of a sufficient criterion for strongly unimodal distribution based on the concept of logarithmic concavity of the distribution density.

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Author Biographies

Yuri P. Virchenko, Belgorod State Technological University named after V. G. Shukhov

Doctor of Physical and Mathematical Sciences, Professor, Professor of the Department of Software for Computing Equipment and Automated Systems, Belgorod State Technological University named after V. G. Shukhov,
Belgorod, Russia
г. Белгород, Россия
E-mail: virch@bsuedu.ru
ORCID: 0000-0002-5413-6179


Amanuel M. Tewolde, Belgorod National Research University

Graduate Student,Belgorod National Research University,
Belgorod, Russia
ORCID: 0009-0006-9669-2858

References

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Ibragimov I. A. On the Composition of Unimodal Distributions. – Theory of Probability and its Applications. – 1956. – 1;2. – P. 255–260.

Rudin W. Principles of Mathematical Analysis / New York: MsGrow-Hill Book Company, 1964. – 320 p.

As Lebesgue-Stieljes Integral /Leizig: G. Teubner Verlagsgesellschaft, 1956. – 328 p.

Virchenko Yu. P., Novoseltsev A. D. Unimodality of probability distributions for sample maximums of the Erlang independent random values.– Belgorod State University Scientific Bulletin. Mathematics & Physics. – 2019. – 51(3). – C. 366–373.

Kolmogorov A. N., Fomin S.V. Elements of the Theory of Functions and Functional Analysis 2 / Albany, New York: Graylock Press, 1961. – 148 p.

Gnedenko B. V., Kolmogorov A. N. Limit Distributions For Sums Of Independent Random Variables / Cambridge: Addison-Wensley Publishing Company, Inc., 1954. – 284 p.

Zorich V. A. Mathematical Analysis I/ New York: Springer-Verlag, 2002. – 552 p.

Virchenko Yu. P., Novoseltsev A. D. Probability distributions unimodality of finite sample extremes of independent Erlang random variables. – Journal of Physics: Conf. Series. – 2020. – 1479. – 012104. doi:10.1088/1742-6596/1479/1/012104.


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Published

2025-09-30

How to Cite

Virchenko, Y. P., & Tewolde, A. M. (2025). Absolutely Continuous, Log-Concave Unimodal Distributions. Applied Mathematics & Physics, 57(3), 208-223. https://doi.org/10.52575/2687-0959-2025-57-3-208-223

Issue

Vol. 57 No. 3 (2025)

Section

Mathematics

Copyright (c) 2025 Applied Mathematics & Physics

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