Unbiased estimation of multi-fractal dimensions of finite data sets

Details Unbiased estimation of multi-fractal dimensions of finite data sets Unbiased estimation of multi-fractal dimensions of finite data sets

1996-02-01

arxiv.org/abs/chao-dyn/9601019v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 17 pages, figures encapsulated as picture environments

Scientific paper

10.1016/S0378-4371(96)00165-3

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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