α稳定分布对称系数和分散系数估计方法

发布时间：2018-03-07 18:11

本文选题：随机信号处理　切入点：参数估计　出处：《华中科技大学学报(自然科学版)》2017年09期 　论文类型：期刊论文

【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α1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α1.8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.
[Abstract]:In this paper, the problem of estimating the symmetric parameters and dispersion coefficients of a stable distribution is studied. A method for estimating symmetric parameters based on limit characteristics and a semi-probabilistic method based on probability distribution function for estimating dispersion coefficients are proposed, respectively. The definition and limit characteristics of 伪 -stable distribution are first introduced. According to the limit characteristics, a method of estimating symmetric parameter 尾 is proposed. The probability distribution function of 伪 stable distribution is introduced by using the ratio of left limit probability to right limit probability of 伪 stable distribution. The properties of probability distribution function are analyzed, and it is pointed out that there is a close relation between the half probability point and 纬 when 伪 1:00. By using this relation, a half probability method for estimating 纬 is proposed. The results show that the estimation error of symmetric parameter estimation method based on limit characteristic is less than 0.05 in most cases of 伪 1.8 and that of semi-probabilistic method is less than 0.02 for 纬.
【作者单位】：吉林大学通信工程学院;中广核研究院有限公司北京分公司;长春理工大学电子信息工程学院;
【基金】：国家自然科学基金资助项目(61571462)
【分类号】：O211.3;TN911.7

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