A new nonparametric test statistic

碩士論文[[abstract]]關於二分配函數是否相等的假設檢定，我們比較熟悉的檢定統計量有Kolmogorov-Smirnov 二樣本檢定統計量（Kolmogorov-Smirnov two-sample test statistic），Cram’er-Von Mises 檢定統計量（Cram’er-Von Mises test statistic）等。而在 1986 年由Katzenbeisser 與 Hackel 提出統計量T，用於兩組樣本數相同時。 隨後，1987年，鄭惟厚與陳奕良推廣統計量T的定義，使之適用於任意樣本數，並提出統計量D。 本論文主要提出一個新的統計量An，並在樣本數相同情況下，導出An的虛無分配。最後再用蒙地卡羅（Monte Carlo）的方法，比較檢定統計量D，An與 Kolmogorov-Smirnov的檢定力（Power）。[[abstract]]Various tests have been proposed for testing the equality of two distribution functions, including the well-known Kolmogorov-Smirnov two-sample test statistic. In 1986, Katzenbeisser and Hackel suggested an alternative statistic T to be used when the sample sizes are equal. Later, in 1987, Wei-Hou Cheng and Yi-Liang Chen found the null distribution of statistic T when sample sizes are unequal. In addition, they proposed a statistic D. In this paper we propose a new test statistic An and derive its null distribution. And we compare the powers of D, An, and Kolmogorov-Smirnov test statistic by the Monte Carlo method