Unbiased estimation of multi-fractal dimensions of finite data sets

A. J. Roberts; A. Cronin

doi:10.1016/s0378-4371(96)00165-3

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arXiv · chao-dyn/9601019

Unbiased estimation of multi-fractal dimensions of finite data sets

A. J. Roberts·A. Cronin

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Abstract

We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well known multi-fractals. By comparing characteristic correlations obtained from the original data with those that occur in artificially generated multi-fractals with the {\em same} number of data points, we expect that predicted multi-fractal properties are unbiased by the finiteness of the experimental data.

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A. J. Roberts, A. Cronin. 1996-02-01. Unbiased estimation of multi-fractal dimensions of finite data sets. https://doi.org/10.1016/s0378-4371(96)00165-3

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