基于样本分位数和log|SαS|的SαS分布参数估计方法

Parameters estimation of symmetric α-stable distribution based on quantiles of samples and log|SαS| method

α稳定分布是一类重要的非高斯随机分布,广泛应用于水声、大气和生物医学信号处理等领域。α稳定分布的特征函数由α、β、γ和a等4个参数决定,因此对于参数的估计具有极其重要的作用。由于α稳定分布没有闭合形式的概率密度函数,大多数传统的依赖于显示密度函数的数学统计方法不再适用。本文分别采用基于样本分位数法和log|SαS|法对SαS分布的α和γ参数进行估计,克服了传统方法中依赖概率密度函数的缺点,仿真结果显示两种算法均能给出较好的估计结果,并且能够满足后期研究的需要。

α-stable distribution is a sort of important non-Gaussian random distribution and is widely applied to water sound, at- mosphere and biomedicine signal processing field and so on. Its characteristic function is determined by the parameters α,β,γ and a, therefore it is important to estimate the parameters. Most of traditional methods based on the probability density function can not be applied because α-stable distribution has not the closed probability density function（PDF）. In this paper, we estimate the parameters α and γ of SαS distribution based on quantiles of samples method and log｜SαS｜ method. The two methods overcome the shortcomings of traditional methods based on PDF. The computer simulations show that the two methods both can give better estimated results and the results can satisfy the needs of the study.