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Methods of Digital Analysis and Interpretation
Published in Victor Raizer, Optical Remote Sensing of Ocean Hydrodynamics, 2019
where =p denotes equality in statistical sense, ξ(r→) is random field, r→={x,y} is coordinate vector, λ>0 is scaling factor, and H is the Hurst exponent or index (Mandelbrot 1983). The Hurst exponent is a statistical measure used to classify time series; it is calculated by rescaled range analysis (R/S) (e.g.,Addison 1997; Weisstein 2003). The Hurst exponent for high-dimensional fractals can be estimated using algorithm (Carbone 2007).
Applicability of sunspot activity on the climatic conditions of Gilgit-Baltistan region using fractal dimension rescaling method
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2021
Ali Khan, Syed Muhammad Murshid Raza, Sajjad Ali
To start with the relation , the upper and lower bounds of the intervals can be represented by the inequality, . This implies that when the value of Hurst exponent goes over and close enough to 0, the time series behavior will show more jagged structure. The other way to expressing Hurst exponent is that it measures the dimensional smoothness of a fractal time series created by the rescaled range (R/S) analysis of the process of the asymptotic behavior. The estimation of Hurst exponent can be made by the expression, , in that case represents duration of the sample data and R/S is the corresponding value of the rescaled range. Rescaled range also measures the divergence of time series in the form as the range of the mean-centered values for a given time period divided by the standard deviation for that duration. In the compact form Hurst suggested how to compute the rescaled range as , in this relation k stands for a constant depending on the nature of a time series, (Kale and Butar Butar 2011).
A comparative study on estimation of fractal dimension of EMG signal using SWT and FLP
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2023
A. A. Navish, M. Priya, R. Uthayakumar
A statistical measuring process that calculates the unevenness of a time series is termed as rescaled range analysis (Bassingthwaighte and Raymond 1994) and this will be done by varying the scope of its mean adjusted cumulative deviate series by the standard deviation. The rescaled range can be changed by adjusting the number of observations.