论文标题
时间空间序列差异的自然动力学系统的概率分布
Time-Spatial Serials Differences' Probability Distribution of Natural Dynamical Systems
论文作者
论文摘要
正态分布用作统一的概率分布，但是，我们的研究人员发现，它与现实生活中的动力学系统的数据并不一致。我们收集和分析了自然存在的数据系列（例如，地球环境，黑子，脑波，心电图，有些情况是经典的混乱系统和社交活动）。发现这些数据集的第一或高阶差异的概率密度函数（PDF）是始终如一的脂肪尾钟形曲线，与正态分布CDF的近乎连接线相比，与正常分布的近连线相比，它们相关的累积分布函数（CDF）始终如一。事实证明，此配置文件不是因为数值或测量误差，而t分布是一个很好的近似值。这种PDF/CDF是独立时间和空间序列数据的普遍现象，这将使研究人员重新考虑有关随机动力学模型（例如Wiener Process）的一些假设，因此值得研究。
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data series (e.g., the earth environment, sunspots, brain waves, electrocardiograms, some cases are classic chaos systems and social activities). It is found that the probability density functions (PDFs) of first or higher order differences for these datasets are consistently fat-tailed bell-shaped curves, and their associated cumulative distribution functions (CDFs) are consistently S-shaped when compared to the near-straight line of the normal distribution CDF. It is proved that this profile is not because of numerical or measure error, and the t-distribution is a good approximation. This kind of PDF/CDF is a universal phenomenon for independent time and space series data, which will make researchers to reconsider some hypotheses about stochastic dynamical models such as Wiener process, and therefore merits investigation.
