Estimator of a non-Gaussian parameter in multiplicative log-normal models
Estimator of a non-Gaussian parameter in multiplicative log-normal models
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DOI：
10.1103/physreve.76.041113
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发表时间：
2007-10-01
影响因子：
2.4
通讯作者：
Yamamoto, Yoshiharu
中科院分区：
文献类型：
--
作者：
Kiyono, Ken;Struzik, Zbigniew R.;Yamamoto, Yoshiharu
研究了考虑高斯随机变量和对数正态分布随机变量相乘的乘性对数正态分布模型的非高斯概率密度函数。为了描述充分发展的湍流中两点速度差的概率密度函数，非高斯概率密度函数模型最早由Castaing提出[Physica D 46,177(1990)]。在实际应用中，通过调整单个非高斯参数来逼近实验PDF，该参数对应于模型中对数正态分布变量的对数方差。本文提出了一种基于q阶绝对矩的非高斯参数估计器。为了检验估计量，我们在乘性对数正态模型的框架内引入了两类随机过程。一个是独立且同分布的随机变量序列。另一类是对数正态级联乘法过程。通过对数值生成的时间序列的分析，我们证明了该估计器能够可靠地确定非高斯参数的理论值。本文还从解析和数值两方面研究了乘性对数正态模型中非高斯参数的尺度依赖性。作为估计量的一个应用，我们证明了在S&P500指数波动中观察到的非高斯概率密度函数可以很好地用乘性对数正态模型来描述。
We study non-Gaussian probability density functions (PDF's) of multiplicative log-normal models in which the multiplication of Gaussian and log-normally distributed random variables is considered. To describe the PDF of the velocity difference between two points in fully developed turbulent flows, the non-Gaussian PDF model was originally introduced by Castaing [Physica D 46, 177 (1990)]. In practical applications, an experimental PDF is approximated with Castaing's model by tuning a single non-Gaussian parameter, which corresponds to the logarithmic variance of the log-normally distributed variable in the model. In this paper, we propose an estimator of the non-Gaussian parameter based on the qth order absolute moments. To test the estimator, we introduce two types of stochastic processes within the framework of the multiplicative log-normal model. One is a sequence of independent and identically distributed random variables. The other is a log-normal cascade-type multiplicative process. By analyzing the numerically generated time series, we demonstrate that the estimator can reliably determine the theoretical value of the non-Gaussian parameter. Scale dependence of the non-Gaussian parameter in multiplicative log-normal models is also studied, both analytically and numerically. As an application of the estimator, we demonstrate that non-Gaussian PDF's observed in the S&P500 index fluctuations are well described by the multiplicative log-normal model.