AI 中文总结
本文提出利用间距特征检测多模态的方法，开发了含参数模型、游程分析等的检验方法，结合变点检测器定位间距变化，通过示例验证并总结了总体性能。
AI 中文摘要
单模态变量的间距呈现出底部平坦、尾部快速上升的“U”形；当组合为多模态设置时，各变量尾部之间的过渡会形成间距的局部增大，这些峰值特征表明数据为多模态，而平坦区域则定位模态。我们针对这些特征开发了检验方法，包括基于假设的零单变量分布的参数模型、区间间距符号差中的游程数或最长游程、以及通过游程置换或基于信号差的池的自助样本进行特征重构。我们还尝试结合现有的变点检测器来寻找间距行为发生变化的位置。本文完整描述了间距的处理、模型与检验，给出了应用示例，并总结了其总体性能。
英文摘要
The spacing of a unimodal variate resembles a `U' with a flat bottom and rapidly increasing values in the tails. When combined into multi-modal setups, the transition between variates into their tails forms local increases in the spacing. These peak features signal the data is multi-modal while the flats locate the modes. We develop tests of the features, including parametric models based on an assumed null univariate distribution, the number of runs or longest run in the signed difference of the interval spacing, and feature reconstruction by means of permutations of the runs or bootstrap samples from a pool based on the difference of the signal. We also try combining existing changepoint detectors to look where the behavior of the spacing changes. This paper describes the processing of the spacing and models and tests in full, gives examples of their use, and summarizes the performance in general.
Comments28 pages, 5 figures ; v1 - added arXiv entries to references
