Not many tests exist for testing the equality for two or more multivariate distributions with compositional data, perhaps due to their constrained sample space. At the moment, there is only one test suggested that relies upon random projections. We propose a novel test termed {\alpha}-Energy Based Test ({\alpha}-EBT) to compare the multivariate distributions of two (or more) compositional data sets. Similar to the aforementioned test, the new test makes no parametric assumptions about the data and, based on simulation studies it exhibits higher power levels.

翻译：目前针对两个或多个成分数据的多元分布相等性检验方法较少，这可能是由于其样本空间受限所致。当前仅有一种基于随机投影的检验方法被提出。本文提出了一种新颖的检验方法——α-能量检验（α-EBT），用于比较两个（或多个）成分数据集的多元分布。与前述检验方法类似，新方法无需对数据做出参数假设，且模拟研究表明其具有更高的检验功效。