Many researchers study various test statistics for appropriately dealing with data. The nonparametric one-way analysis of variance plays an important role in biometry. For the multisample location-scale problem, the generalized Cucconi test statistic has been proposed for the location, scale, and location-scale parameters. This study derives the limiting distribution of the suggested test statistic. Computing the exact critical value of the statistic can be difficult when the sample sizes are large. An approximation method regarding the distribution function of the test statistic can be useful in this situation. We use a gamma approximation to evaluate the upper-tail probability of the proposed test statistic for a finite sample size.

中文翻译：

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位置和尺度参数的广义多样本 Cucconi 检验统计量

许多研究人员研究各种测试统计以适当处理数据。非参数单向方差分析在生物测量中起着重要作用。对于多样本位置尺度问题，已针对位置、尺度和位置尺度参数提出了广义 Cucconi 检验统计量。本研究推导出建议检验统计量的极限分布。当样本量很大时，计算统计量的确切临界值可能很困难。在这种情况下，有关检验统计量分布函数的近似方法可能很有用。我们使用伽玛近似来评估有限样本量的建议检验统计量的上尾概率。