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离散分布 Kolmogorov–Smirnov 统计量的大样本结果AI 解读

The asymptotic distributions of the Kolmogorov-Smirnov goodness-of-fit statistics are considered when the hypothesized distribution is discrete. Each of the statistics is shown to have the same distribution as a continuous functional of an associated empirical process on the unit interval. Using known weak convergence properties for the empirical process, the asymptotic distributions of the Kolmogorov-Smirnov statistics are derived. A discussion and example are included.

随机区组设计中实验误差正态性的大样本 KS 检验AI 解读

The weak convergence of the sample distribution function based on the estimated residuals in a randomized block design is considered under the null hypothesis of normality of the experimental errors. This result serves as a basis for deriving the limiting distribution of the Kolmogorov-Smirnov statistic computed from the estimated residuals. Quantiles of Monte Carlo simulations of the limiting distributions for various numbers of treatments are given. These results are…

离散分布下Kolmogorov–Smirnov统计量的大样本结果AI 解读

The asymptotic distributions of the Kolmogorov-Smirnov goodness-of-fit statistics are considered when the hypothesized distribution is discrete. Each of the statistics is shown to have the same distribution as a continuous functional of an associated empirical process on the unit interval. Using known weak convergence properties for the empirical process, the asymptotic distributions of the Kolmogorov-Smirnov statistics are derived. A discussion and example are included.