Exploring the Statistical Properties of Outputs from a Process Inspired by Geometrical Interpretation of Newton's Method
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910526493163520 |
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| author | Kirouani, Taki |
| author_facet | Kirouani, Taki |
| contents | In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its distribution. Through rigorous mathematical proof, we demonstrate that the probability density function follows a Cauchy distribution. Additionally, a new method to generate a uniform distribution is proposed. To further confirm our findings, we employed statistical tests, including the Kolmogorov-Smirnov test and Anderson-Darling test, which showed high p-values. Furthermore, we show that the distribution of the distance between two successive outputs can be obtained through a transformation method applied to the Cauchy distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring the Statistical Properties of Outputs from a Process Inspired by Geometrical Interpretation of Newton's Method Kirouani, Taki Data Analysis, Statistics and Probability Probability Statistics Theory In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its distribution. Through rigorous mathematical proof, we demonstrate that the probability density function follows a Cauchy distribution. Additionally, a new method to generate a uniform distribution is proposed. To further confirm our findings, we employed statistical tests, including the Kolmogorov-Smirnov test and Anderson-Darling test, which showed high p-values. Furthermore, we show that the distribution of the distance between two successive outputs can be obtained through a transformation method applied to the Cauchy distribution. |
| title | Exploring the Statistical Properties of Outputs from a Process Inspired by Geometrical Interpretation of Newton's Method |
| topic | Data Analysis, Statistics and Probability Probability Statistics Theory |
| url | https://arxiv.org/abs/2407.09583 |