Finite mixtures offer a rich class of distributions for modelling of a variety of random phenomena in numerous fields of study. Using the sample interpoint distances (IPDs), we propose the IPD‐test statistic for testing the hypothesis of homogeneity of mixture of multivariate power series distribution or multivariate normal distribution. We derive the distribution of the IPDs that are drawn from a finite mixture of the multivariate power series distribution and multivariate normal distribution. Based on the empirical distribution of the IPDs, we construct a bootstrap test of homogeneity for other multivariate finite mixture models. The IPD test is applied to mixture models for matrix‐valued distributions and a test of homogeneity for Wishart mixture is presented. Numerical comparisons show that IPD test has accurate type I errors and is more powerful in most multivariate cases than the expectation–maximization (EM) test and modified likelihood ratio test.

中文翻译：

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多元混合物模型同质性的点间距离检验

有限混合物为许多研究领域中的各种随机现象的建模提供了丰富的分布类别。使用样本点间距离（IPD），我们提出了IPD检验统计量，用于检验多元幂级数分布或多元正态分布的混合均匀性的假设。我们从多元幂级数分布和多元正态分布的有限混合中得出IPD的分布。基于IPD的经验分布，我们构造了其他多元有限混合模型的同质性自举测试。IPD测试应用于矩阵值分布的混合物模型，并提出了Wishart混合物的均匀性测试。