Log-amplitude statistics for Beck-Cohen superstatistics
Log-amplitude statistics for Beck-Cohen superstatistics
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Beck-Cohen 超级统计的对数振幅统计
DOI：
10.1103/physreve.87.052104
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
H. Konno
中科院分区：
文献类型：
--
作者：
K. Kiyono;H. Konno
作为Beck-Cohen超统计过程的一种可能的推广，我们研究了具有局部方差时间异质性的非高斯过程。为了表征方差的异质性，我们定义了对数振幅累积量和对数振幅自协方差，并推导出对数振幅累积量的封闭形式的表达式，逆，对数正态超统计分布。此外，我们还证明了度为2的统计量和逆统计量与一个极值分布密切相关，称为Gumbel分布。在这些情况下，相应的超统计分布的结果，在高斯分布和双边指数分布，分别。因此，我们的发现提供了一个假设，这两个特殊的分布的渐近外观可以解释与渐近极限分布涉及极值的链接。此外，作为我们的方法的应用，我们证明了在股票指数期货市场中观察到的非高斯波动可以很好地近似的degree为2的统计分布。
As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for, inverse, and log-normal superstatistical distributions. Furthermore, we show thatand inversesuperstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the-Gaussian distribution withand the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by thesuperstatistical distribution with degree 2.