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：针对两个或多个具有成分数据的多元分布进行相等性检验的方法并不多见，这或许源于其受限的样本空间。目前，仅有一种基于随机投影的检验方法被提出。我们提出了一种称为{\alpha}-能量检验（{\alpha}-EBT）的新方法，用于比较两个（或多个）成分数据集的多元分布。与前述检验类似，新方法不对数据作参数化假设，且模拟研究表明其具有更高的检验功效。