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Statistical error in a chord estimator of correlation dimension: the ``rule of five''

James Theiler·Turab Lookman
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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

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James Theiler, Turab Lookman. 1993-02-26. Statistical error in a chord estimator of correlation dimension: the ``rule of five''. https://doi.org/10.1142/s0218127493000672

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