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拟合优度统计量 V_NN 分布的渐近展开
The complete asymptotic expansion in powers of $N^{-\frac{1}{2}}$ for the distribution of the two-sample statistic $V_{NN}$ is derived under the null hypothesis. The proof is based on methods developed by Kemperman (1959).
分组数据的拟合优度检验
Following Riedwyl [8] we generalize some one-sample statistics of the Cramér-von Mises type so that they can be used to test grouped data for goodness of fit. We prove that under the null hypothesis the asymptotic distributions of these statistics, when suitably standardized, coincide with the corresponding classical statistics if the ratio of the sample size to the number of groups (k) remains constant. For k fixed the asymptotic distributions are given under the null…
关于 Kolmogorov–Smirnov 型单样本统计量
Asymptotic expansions with a term in n−½ of the distributions of Pyke's modified one-sample Kolmogorov-Smirnov statistics, C+n, C−n and Cn are derived. From these expansions and the already known ones for D+n, D−n, Dn, Vn = D+n + D−n and Kn = C+n + C−n are deduced expansions for the percentage points. The approximate percentage points determined by these expansions are sufficiently accurate to be used in applications.
Watson 统计量的 k 样本推广
The statistics UN2 and UN,M2,, introduced by Watson (1961, 1962), are particularly suited to test for goodness-of-fit when the observations are taken on the circumference of a circle. In this paper, extensions of these tests to k samples, are given and the limiting distributions under the null hypotheses are derived and tabulated.