α稳定分布对称系数和分散系数估计方法  

Method to estimate index of skewness and dispersion ofα-stable distribution

作　　者：关济实[1,2] 石要武 邱建文[2] 史红伟 

机构地区：[1]吉林大学通信工程学院,吉林长春130025 [2]中广核研究院有限公司北京分公司,北京100083 [3]长春理工大学电子信息工程学院,吉林长春130022

出　　处：《华中科技大学学报（自然科学版）》2017年第9期23-27,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61571462)

摘　　要：研究了α稳定分布的对称参数和分散系数估计问题,分别提出了基于极限特征的对称参数估计方法和用于估计分散系数的基于概率分布函数的半概率法.首先介绍了α稳定分布的定义和极限特征,并根据极限特征提出一种估计对称参数β的方法,该方法利用α稳定分布的左极限概率与右极限概率的比值来估计β.介绍了α稳定分布的概率分布函数,分析了概率分布函数的性质,并指出当α>1时,半概率点与γ之间有紧密的联系,并利用这一联系,提出一种估计γ的半概率方法.通过仿真实验验证了以上两种估计方法,结果表明:基于极限特征的对称参数估计方法当α<1.8时多数情况下估计误差小于0.05,半概率方法对γ的估计误差小于0.02.Method for index of skewness （β）and scale parameter （γ）estimation ofα-stable distribu-tion was studied.Method to estimateβthat based on extreme character ofα-stable distribution and method to estimateγbased on the half probability point ofα-stable distribution probability distribu-tion function （PDF）were proposed.Definition and extreme property ofα-stable distribution was in-troduced.According to the extreme property,the ratio of left and right extreme probability was used to estimateβparameters ofα-stable distribution.Probability distribution function ofα-stable distribu-tion was introduced and the property of PDF was analyzed.The half probability point of PDF is close-ly related to theγparameter ofα-stable distribution whenα＆gt;1 .Based on this property,the half prob-ability point method to estimateγwas proposed.Simulation experiment show thatβestimation error of the method based on extreme property is lower than 0.05 under mostly condition whenα＆lt;1.8 and theγestimation error of the half probability point method is lower than 0.02.

关 键 词：随机信号处理 参数估计 Α稳定分布 对称系数 分散系数 极限特征 概率分布函数 

分 类 号：TP911.72[自动化与计算机技术]