Unbiased estimation of multi-fractal dimensions of finite data sets
Abstract
We present a novel method for determining multi-fractal properties from experimental data. It is based on maximizing 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 same number of data points, we expect that predicted multi-fractal properties are unbiased by the finiteness of the experimental data.
- Publication:
-
Physica A Statistical Mechanics and its Applications
- Pub Date:
- February 1996
- DOI:
- 10.1016/S0378-4371(96)00165-3
- arXiv:
- arXiv:chao-dyn/9601019
- Bibcode:
- 1996PhyA..233..867R
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- LaTeX, 17 pages, figures encapsulated as picture environments