Exploring the Statistical Properties of Outputs from a Process Inspired by Geometrical Interpretation of Newton's Method
Abstract
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.
Keywords
Cite
@article{arxiv.2407.09583,
title = {Exploring the Statistical Properties of Outputs from a Process Inspired by Geometrical Interpretation of Newton's Method},
author = {Taki Kirouani},
journal= {arXiv preprint arXiv:2407.09583},
year = {2024}
}