Complexity researchers view burstiness--fluctuating levels of activity--as evidence of hidden interactions within the system generating the activity signal. Yet, current burstiness metrics miss evidence of burstiness in some moderately bursty distributions and under moderate sampling conditions. The canonical Burstiness Parameter (BP) compares distributions of timing statistics to the exponential distribution, representing the timing of independent random events, but it provides false negatives for some parameter ranges of power laws, with and without cut-offs. We introduce a metric that maintains BP's measurement approach but reduces false negatives: the Burstiness Tail-based Index (BTI). Based on ratios of differences in quantiles, BTI correctly classifies bursty distributions over certain parameter ranges misclassified by BP. Additionally, we find BTI to be more robust than BP in the presence of limited sample sizes and short observation windows, using simulated samples drawn from distributions correctly classified by BP in their analytical form. As a case study, we revisit an analysis of human activity data and find that the choice of BTI over BP influences interpretations of the timescales of burstiness in the dataset. Given these analytical, simulated, and empirical results, we argue for BTI's practical advantage over BP in assessing burstiness in real-world temporal signals for complexity research and time series modeling.

翻译：复杂性研究者将突发现象——活动水平的波动——视为系统内部隐藏相互作用的证据。然而，当前的突发性指标在部分中等突发分布及中等采样条件下会遗漏突发证据。经典突发参数（BP）将时序统计量的分布与代表独立随机事件时序的指数分布进行比较，但在无界幂律及有截断幂律的某些参数范围内会产生假阴性结果。我们引入一种保持BP测量思路但降低假阴性的新指标：基于尾部分位数的突发指数（BTI）。通过利用分位数差值的比值，BTI能正确识别被BP误判的某些参数范围内的突发分布。此外，我们利用从BP解析形式正确分类的分布中抽取的模拟样本发现，在有限样本量和短观测窗口条件下，BTI比BP更具鲁棒性。作为案例研究，我们重新分析了人类活动数据，发现使用BTI而非BP会改变对数据集中突发时间尺度的解释。基于这些解析、模拟及实证结果，我们论证了在复杂性研究和时间序列建模中，BTI相较于BP在评估真实世界时间信号的突发现象时具有实践优势。