Data Curve Fitting for Power Law Distribution Analysis

In MATLAB, data curve fitting can be performed using various methods such as linear least squares, nonlinear least squares, and other regression techniques. When working in log-log coordinates, one can determine whether data follows a power law distribution by comparing the fitted curve against actual data points. A key implementation approach involves applying logarithmic transformation to both variables (log(x) and log(y)) before performing linear regression, where the resulting slope corresponds to the power exponent. If the data conforms to a power law distribution, the power exponent obtained through fitting reveals critical characteristics about the underlying data pattern. Essential MATLAB functions for this process include polyfit for linear regression in logarithmic space, or fitnlm for more complex nonlinear power law models. Furthermore, visualization can be enhanced by plotting both the fitted curve and original data points using semilogx/semilogy or loglog functions, with customization options for line styles and markers to improve graphical distinction. This comprehensive approach provides intuitive representation of distribution patterns while maintaining statistical rigor through quantitative fitting metrics.