the modified form of the gutenberg-richter law in solar flare complex network : approach of genetic algorithm on the thresholded power-law behavior

The hybrid model approach is adopted to construct the solar are complex network. the modified form of gutenberg-richter law is obtained as the frequency- magnitude distribution of the empirical data. the frequency-magnitude distributions of positive-definite data are sometimes observed to follow a power-law over several orders of size. there are reasons to the deviation of the frequency-magnitude distribution from an ideal power distribution. among many alternative forms of the power-law function, we found that the threshold power-law is well fifted with solar empirical data at small values. a statistical method based on optimization of the x^2-test by application of the genetic algorithm has been developed. here, the analytical details of a method based on genetic algorithm is presented to calculate the parameters of the frequency-magnitude distribution of the empirical data sets. this method estimates the best parameters of the threshold power-law function as the frequency- magnitude distribution of the empirical data, as well.