Fractal-dimensions (D) and Hurst-exponent (H) are often used for determining a randomness (RI) or predictability index in distributed signals, from the linear relationship of RI = 1–H = D–1, as H+D = 2. This paper investigates the similarities and differences of the results of different methods, when calculating D, H, and RI with the same dataset signals. 8 different methods were tested: Higuchi's (D), Saupe's Variance (H), Dispersional (H), Rescaled-Adjusted-Range R/S (H), Detrended-Fluctuation-Analysis DFA (H), Runs (RI), Persistence-Antipersistence (RI), and ¼-Variance-ratio (RI). These methods were tested with distributed datasets, namely (1) fractional Gaussian noise and its time derivatives, (2) datasets of expected RI, and (3) an EEG signal. All D and H data were converted to RI. For datasets (1), all methods performed equally well for datasets of H = 0.5, although the standard deviations of some methods were greater than 0.02. For datasets (2), applied only to RI methods, Runs and Persistence-Antipersistence methods were accurate. All 8 methods performed reasonably well when processing the EEG signal. The relationship between RI and H and D is not a linear one and rather follows the square root of a quadratic function. From this function, however, the actual RI (calculated from RI methods) is not defined if the expected RI (obtained from H and D methods via a linear relationship) equals 1. In this case, the actual RI can be anywhere between 2/3 and 1. Therefore, we suggest, based on the results of this study, that the RI is inaccurately and incompletely determined when using the detour via H & D methods, and that the RI is accurately and directly derived from the Runs or RI p-ap methods, which should be used when the RI, and associated parameters such as persistence, anti-persistence, and predictability are of interest.

分形维数（D）和赫斯特指数（H）通常用于根据RI = 1–H = D–1的线性关系来确定分布信号中的随机性（RI）或可预测性指标，因为H + D = 2.本文研究了在使用相同数据集信号计算D，H和RI时，不同方法的结果的异同。测试了8种不同的方法：gu口（D），索普方差（H），色散（H），重标调整范围R / S（H），去趋势分析法DFA（H），运行（RI），持久性-反持久性（RI）和1/4方差比（RI）。这些方法已通过分布式数据集进行了测试，即（1）分数高斯噪声及其时间导数，（2）预期RI数据集和（3）EEG信号。所有D和H数据都转换为RI。对于数据集（1），尽管某些方法的标准偏差大于0.02，但对于H = 0.5的数据集，所有方法的效果均相同。对于仅应用于RI方法的数据集（2），Runs和Persistence-Antipersistence方法是准确的。在处理EEG信号时，所有8种方法均表现良好。RI与H和D之间的关系不是线性关系，而是遵循二次函数的平方根。但是，根据此函数，如果预期RI（通过线性关系从H和D方法获得）的预期RI等于1，则未定义实际RI（根据RI方法计算）。在这种情况下，实际RI可以在2 / 3和1。因此，根据本研究的结果，我们建议在通过H＆D方法绕行时确定RI不准确和不完整，