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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Skewed distributions as limits of a formal evolutionary process
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Skewed distributions as limits of a formal evolutionary process

机译：偏斜的分布为正式进化过程的限制

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摘要

Time series of observables measured from different turbulent systems do often exhibit nonnormal statistics, their probability distribution functions (PDFs) are not Gaussian and often skewed, with roughly exponential tails, skewness and kurtosis. Departure from gaussianity is related to the intermittent development of large-scale coherent structures. The existence of these structures is rooted into the nonlinear dynamical equations obeyed by each system, therefore it is expected that some prior knowledge or guessing of these equations is needed if one wishes to infer the corresponding PDF; conversely, the empirical knowledge of the PDF does provide information about the underlying dynamics. In this work we advance the suggestion that this is not always necessary. We show that, under some assumptions, a formal evolution equation for the PDF p(x) can be written down, corresponding to the progressive accumulation of measurements of the generic observable x. The limiting solution to this equation is computed analytically, and shown to interpolate between some of the most common distributions, Gamma, Beta and Gaussian PDFs. The control parameter is just the ratio between the root mean square of the fluctuations and the range of allowed values. Thus, no information about the dynamics is required.
机译：从不同湍流系统测得的观测数据的时间序列通常表现出非正态统计特性，其概率分布函数（PDF）不是高斯分布，通常是偏态的，具有大致的指数尾、偏度和峰度。偏离高斯性与大尺度相干结构的间歇性发展有关。这些结构的存在植根于每个系统所遵循的非线性动力学方程，因此，如果希望推断相应的PDF，则需要对这些方程进行一些先验知识或猜测；相反，PDF的经验知识确实提供了有关基本动态的信息。在这项工作中，我们提出的建议是，这并不总是必要的。我们证明，在某些假设下，PDF p（x）的形式演化方程可以写下来，对应于一般可观测x的测量值的累进累积。该方程的极限解通过解析计算，并显示在一些最常见的分布，伽马、贝塔和高斯PDF之间插值。控制参数只是波动的均方根与允许值范围之间的比率。因此，不需要关于动力学的信息。

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