249.

[Cover] [Abbreviated Contents] [Contents] [Index]

Page 98
1.5.13—
How to Measure the Properties of Fractal Data
The statistical properties, such as the average or variance, of a fractal object or process depend on the resolution used to measure them. Thus it does little good to measure these statistical properties at only one resolution.
The meaningful measurement is to determine how these statistical properties depend on the resolution used to measure them.
Usually, the scaling relationship for a statistical property c0030-01.gif will have the power law form that c0030-01.gif is proportional to rb, where r is the resolution. The exponent b is related to the fractal dimension.
A number of different statistical properties c0030-01.gif have been used to analyze fractal data, including the:
1. mean (average);
2. variance;
3. standard deviation;
4. relative dispersion (standard deviation/variance);
5. Fano factor (variance/mean);
6. mean squared deviation; and
7. rescaled range (range of the running sum of the deviations from the mean divided by the standard deviation).

 
[Cover] [Abbreviated Contents] [Contents] [Index]


Fractals and Chaos Simplified for the Life Sciences
Fractals and Chaos Simplified for the Life Sciences
ISBN: 0195120248
EAN: 2147483647
Year: 2005
Pages: 261

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