Alpha稳定分布的参数表征及仿真

Parameterizations and Simulation of Alpha stable Distribution

仿真服从标准参数系下任意参数的Alpha稳定分布(αS)随机变量是开展相关信号处理研究的基础。服从对称Alpha稳定分布(SαS)的随机变量较易生成,而产生服从αS分布随机变量较为困难,一个重要的因素是存在易于混淆的不同参数表征。本文在讨论Alpha稳定分布概念、性质的基础上,讨论了三种主要参数系,提出并证明了正确的产生服从αS分布随机变量的变换公式及仿真方法,并通过Monte-carlo仿真比较了三种参数系表征的αS分布的概率密度函数的差异。对Pearson海杂波的仿真表明了该方法的有效性,而Chambers方法存在分布位置的偏差。

Simulating random variable （r. v. ） subject to Alpha stable distribution with arbitrary parameters in the standard parameterization （αS） is the foundation to perform some research on signal processing. There are different parameterizations for Alpha stable distribution that are easy to cause confusion. For this reason, the r. v. subject to aS is more difficult to generate than that with symmetric 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 to aS, 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.