Alpha稳定分布参数评估及应用研究
首发时间:2013-04-02
摘要:随着信号处理技术的发展,非高斯信号处理是近年来发展起来的一个信号处理的新领域。基于广义中心极限定理的Alpha稳定分布是一种广义的高斯分布,它能够很好的描述信号统计分布的非高斯性和重拖尾性。本文首先讨论Alpha稳定分布的定义和基本理论;然后求解出该分布的概率密度函数以便于样本分位数法和基于分数低阶矩法的实现;最终,把研究结果应用于上证指数和道琼斯工业指数,求解出其服从的分布模型。
关键词: Alpha稳定分布 参数估计 非高斯 样本分位数法 分数低阶矩法
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Research on Parameters Estimation and Application of Alpha-Stable Distributions
Abstract:Non-Gaussian signal processing is a new signal processing field with the development of signal processing techniques in recent years. The Alpha stable distribution, which is a kind of generalized Gaussian distribution, has the statistical characteristics of non-Gaussian and heavy tailed. Firstly, the definitions and basic theories of the Alpha stable distribution are discussed. Secondly, compute the probability density function value to implement Fractional Lower Order Moment method and the Sample Quintiles' method easily. Finally, the Alpha stable distribution is used in Shanghai composite Index and Dow Jones Industrial Average, and the related parameters are estimated.
Keywords: Alpha stable distribution Parameter estimation Non-Gaussian Sample quantiles method Fractional Lower Order Moment method
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