Parameterizations and Simulation of Alpha stable Distribution
Xutao Li · Signal Processing · 2007
Simulating random variable(r.v.)subject to Alpha stable distribution with arbitrary parameters in the standard pa- rameterization(αS)is the foundation to perform some research on signal processing.There are different parameterizations for Alpha sta- ble distribution that are easy to cause confusion.For this reason,the r.v.subject toαS is more difficult to generate than that with sym- metric Alpha stable distribution(SαS).Based on the concepts and properties of the Alpha stable distribution,the three parameterizations are discussed.Furthermore,we propose and proof the equation to accurately generate the r.v.subject toαS,as well as the simulation method.The PDF of parameterizations are compared by Monte-carlo simulation.Finally,the simulations for Pearson sea-clutter show that our method is valid and the method of Chambers has a certain error.