Issue |
E3S Web Conf.
Volume 587, 2024
International Scientific Conference on Green Energy (GreenEnergy 2024)
|
|
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Article Number | 01021 | |
Number of page(s) | 14 | |
Section | Energy Production, Transmission, Distribution and Storage | |
DOI | https://doi.org/10.1051/e3sconf/202458701021 | |
Published online | 07 November 2024 |
Poisson approximation of binomial point processes
1 National University of Uzbekistan, Tashkent, Uzbekistan
2 Tashkent State Transport University, Tashkent, Uzbekistan
* Corresponding author: khamdamov.isakjan@gmail.com
In the paper, we study properties of the vertex process from convex hulls generated by independent observations of a two-dimensional random vector, the distribution of which behaves like a regularly varying function near the boundary of the support of the disk. The problem of approximating the distributions of sums of random variables, despite its rich history, is still relevant today. The Poisson approximation, along with the normal approximation, remain intensively developing areas of modern probability theory. We note their importance in solving statistical problems, in which the presence of a simple asymptotic expansion makes it possible not only to obtain more accurate statistical estimates, but also to solve the problem of the error significance level. In this article, we use the Poisson approximation to study the limit distributions of functionals generated by aninhomogeneous binomial point process.
© The Authors, published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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