Comparison of two fractal dimension estimation methods in predicting fracture risk in vertebrae

1996 ◽  
Vol 6 (S1) ◽  
pp. 146-146 ◽  
Author(s):  
J. F. Veenland ◽  
T. M. Link ◽  
W. Konermann ◽  
N. Meier ◽  
J. L. Grashuis ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fracture Risk ◽  
Estimation Methods ◽  
Dimension Estimation

EFFECT OF OUTLIERS ON THE FRACTAL DIMENSION ESTIMATION

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 233-241
Author(s):  
SHAPOUR MOHAMMADI
Keyword(s):  
Fractal Dimension ◽  
Stock Prices ◽  
Time Series Data ◽  
Estimation Method ◽  
Estimation Methods ◽  
Series Data ◽  
Data Series ◽  
Box Dimension ◽  
Dimension Estimation ◽  
Stochastic Data

The effect of outliers on estimation of the fractal dimension of experimental chaotic and stock market stochastic data series is investigated. The results indicate that influential observations of a magnitude of mean ±5 standard deviations can lead to a distortion of fractal dimension estimations by as much as 40% for short (e.g. 500 observations) time series data. Moreover, the box dimension estimation method is more sensitive to outliers than information and correlation dimension estimation methods and the effect of outliers decreases as the number of observations increases. Application of outlier adjustment to the stock prices of 60 companies of the Dow Jones Industrial Index reveals that the effect of outliers is critical in estimating the fractal dimension. The fractal dimension has applications in risk analysis for financial markets that can be affected by outliers.

scholarly journals A Stochastic Model for the Fractal Dimension Estimation of Asphaltenes Aggregation

2019 ◽  
Vol 8 (6) ◽  
pp. 1992-1995
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Stochastic Model ◽  
Production Systems ◽  
Experimental Results ◽  
Crude Oils ◽  
Dimension Estimation ◽  
Maximum Value ◽  
Solids Deposition

Some of the problems associated with the transportation of crude oils are due to the presence of heavy compounds as asphaltene molecules. This work developed a stochastic model that predicts the fractal dimension of the asphaltene aggregates. It was found that the maximum value of the fractal dimension is 1.71, which corresponds to the reported experimental results. The model can be applied as a universal growing behavior for the analysis of surface roughness when solids deposition is observed in the production systems involving crude oils

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