Statistical error in a chord estimator of correlation dimension: the ``rule of five''
comp-gas
2019-06-05 v1 Cellular Automata and Lattice Gases
Abstract
The statistical precision of a chord method for estimating fractal dimension from a correlation integral is derived. The optimal chord length is determined, and a comparison is made to other estimators. These calculations use the approximation that all pairwise distances between the points are statistically independent; the adequacy of this approximation is assessed numerically. The chord method provides a very quick and easy dimension estimate which is only slightly less precise than the optimal estimator. Keywords: correlation dimension, statistical error
Keywords
Cite
@article{arxiv.comp-gas/9302002,
title = {Statistical error in a chord estimator of correlation dimension: the ``rule of five''},
author = {James Theiler and Turab Lookman},
journal= {arXiv preprint arXiv:comp-gas/9302002},
year = {2019}
}
Comments
CYCLER Paper 93feb010 Compress'ed PostScript file