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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.23830 |
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| _version_ | 1866917047674339328 |
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| author | Bhattacharjee, Syon Dhar, Subhra Sankar |
| author_facet | Bhattacharjee, Syon Dhar, Subhra Sankar |
| contents | This article studies statistical estimation of $π$ based on the fact that the ratio of the volumes of a $d$-dimensional hypersphere and a $d$-dimensional hypercube is a certain function of $π$, and the function depends on the dimension $d$. The estimation of $π$ is carried out for various choices of $d$ (strictly speaking, $d\in\{1, 2, \ldots, 20\}$) using the idea of Monte Carlo simulations. Various intriguing facts are observed, and the estimation of $π$ using infinite dimensional observations is outlined. Moreover, the R codes associated with relevant numerical studies are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical estimation of $π$: varying choices over dimensions Bhattacharjee, Syon Dhar, Subhra Sankar Other Statistics This article studies statistical estimation of $π$ based on the fact that the ratio of the volumes of a $d$-dimensional hypersphere and a $d$-dimensional hypercube is a certain function of $π$, and the function depends on the dimension $d$. The estimation of $π$ is carried out for various choices of $d$ (strictly speaking, $d\in\{1, 2, \ldots, 20\}$) using the idea of Monte Carlo simulations. Various intriguing facts are observed, and the estimation of $π$ using infinite dimensional observations is outlined. Moreover, the R codes associated with relevant numerical studies are provided. |
| title | Statistical estimation of $π$: varying choices over dimensions |
| topic | Other Statistics |
| url | https://arxiv.org/abs/2510.23830 |