标题： 方向统计学中的框架理论 显示英文标题

标题： Frame theory in directional statistics

摘要： 在方向数据分析中，区分均匀和非均匀样本分布是一个常见问题；然而，对于许多检验方法而言，存在一些非均匀分布能够通过均匀性检验。通过将方向统计学与框架理论相结合，我们发现概率紧框架会产生最小化方向势能的非均匀分布，这导致了Bingham检验中均匀性检验的失败。最后，我们将我们的研究成果应用于模拟粒状棒实验中观察到的模式。 显示英文摘要

摘要： Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics with frame theory, we find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments.