The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties—pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one. The dependence of the signal samples is achieved by moving average filter and non-linear equations. The applied coupling methods are checked using statistical tests for correlation. The changes in signal regularity are checked by a multifractal spectrum. The probability integral transformation is then applied to cardiovascular time series—systolic blood pressure and pulse interval—acquired from the laboratory animals and represented the results of entropy estimations. We derived an expression for the reference value of entropy in the probability integral transformed signals. We also experimentally evaluated the reliability of entropy estimates concerning the matching probabilities.

中文翻译：

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关于概率积分变换时间序列的熵


本文的目的是研究当使用概率积分变换均衡时间序列的幅度分布时熵估计的变化。我们分析的数据具有已知的属性——具有已知分布的伪随机信号，使用统计或确定性方法相互耦合，包括统计相关分布的生成器、线性和非线性变换以及确定性混沌。使用范围从 0 到 1 的相关系数来耦合信号对。信号样本的相关性是通过移动平均滤波器和非线性方程来实现的。使用相关性统计测试来检查所应用的耦合方法。通过多重分形谱检查信号规律性的变化。然后将概率积分变换应用于从实验动物获得的心血管时间序列（收缩压和脉搏间隔）并表示熵估计的结果。我们推导了概率积分变换信号中熵的参考值的表达式。我们还通过实验评估了有关匹配概率的熵估计的可靠性。