MATLAB Implementation of Alpha-Stable Distribution Noise

There are multiple approaches to implement alpha-stable distribution noise in MATLAB. One primary method involves using the "stabrnd" function, which directly generates random numbers following the alpha-stable distribution by specifying characteristic exponent (α), skewness (β), scale (γ), and location (δ) parameters. An alternative approach utilizes the "alpha_rnd" function from the SFS (Statistical and Financial Software) package, which implements Chambers-Mallows-Stuck method for efficient alpha-stable variate generation. Additionally, researchers can employ the "stable_pdf" function to compute the probability density function of alpha-stable distributions, enabling analytical verification of generated noise properties. These implementation methods support various applications including financial modeling, signal processing, and robust statistical analysis where heavy-tailed noise characteristics are required. The code typically involves parameter configuration, random number generation, and optional validation through distribution fitting tests.