A multi-sample test for equality of mean directions is developed for populations having Langevin-von Mises-Fisher distributions with a common unknown concentration. The proposed test statistic is a monotone transformation of the likelihood ratio. The high-concentration asymptotic null distribution of the test statistic is derived. In contrast to previously suggested high-concentration tests, the high-concentration asymptotic approximation to the null distribution of the proposed test statistic is also valid for large sample sizes with any fixed nonzero concentration parameter. Simulations of size and power show that the proposed test outperforms competing tests. An example with three-dimensional data from an anthropological study illustrates the practical application of the testing procedure.

中文翻译：

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Langevin-von Mises-Fisher 分布平均方向相等性的改进检验

针对具有常见未知浓度的 Langevin-von Mises-Fisher 分布的群体开发了平均方向相等的多样本检验。建议的检验统计量是似然比的单调变换。推导出检验统计量的高浓度渐近零分布。与先前建议的高浓度测试相比，建议的测试统计量的零分布的高浓度渐近近似对于具有任何固定非零浓度参数的大样本量也有效。大小和功率的模拟表明，所提出的测试优于竞争测试。一个来自人类学研究的三维数据示例说明了测试程序的实际应用。