Ball: An R Package for Detecting Distribution Difference and Association in Metric Spaces

The rapid development of modern technology has created many complex datasets in non-linear spaces, while most the statistical hypothesis tests are only available Euclidean or Hilbert spaces. To properly analyze data with more complicated structures, efforts have been made to solve fundamental test problems general spaces (Lyons 2013; Pan, Tian, Wang, and Zhang 2018; Zhang, Zhu, Zhu 2020). In this paper, we introduce a publicly R package Ball for comparison multiple distributions mutual independence metric which extends procedures equality two (Pan et al. 2018) random objects is computationally efficient since several novel algorithms as well engineering techniques employed speeding up ball procedures. Two real analyses diverse numerical studies performed, results certify that can detect various distribution differences dependencies datasets, e.g., directional symmetric positive definite matrix data.