tailieunhanh - Handbook of mathematics for engineers and scienteists part 163

Handbook of mathematics for engineers and scienteists part 163. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | 1102 Mathematical Statistics where m is the number of degrees of freedom. If prom - 3 then the null hypothesis should be accepted if prom 3 then the null hypothesis should be rejected. This test has a fixed size a . 2 . Test for excluding outliers. To test the null hypothesis the following statistic is used x max Xi - m S 1-i-n where s is the sample mean-square deviation. The null hypothesis H0 for a given size a is accepted if x x1-a where xa is the quantile of the statistic x under the assumption that the sample is normal. The values of xa for various n and a can be found in statistical tables. 3 . Test based on the sample first absolute central moment. The test is based on the statistic 1 O H X1 . xn V X - m . ns i 1 Under the assumption that the null hypothesis H0 is true the distribution of the statistic 1 depends only on the sample size n and is independent of the parameters a and a2. The null hypothesis H0 for a given size a is accepted if ia 2 1 11-a 2 where ia is the a-quantile of the statistic p . The values of pa for various n and a can be found in statistical tables. 4 . Test based on the sample asymmetry coefficient. The test is based on the statistic 1 n 71 y Xi . Xra - 3 V Xi - m 3. n s 3 The null hypothesis H0 for a given size a is accepted if y Yi i-a 2 where 71 a is the a-quantile of the statistic 7 . The values of Y1 a for various n and a can be found in statistical tables. 5 . Test based on sample excess coefficient. excess the test statistic The test verifies the closeness of the sample 7 72 X1 . Xn 1 ------r V Xi - m 4 n s 4 1 and the theoretical excess Y2 3 E X - E X 4 Var X 2 equal to 3 for the normal law. The null hypothesis H0 for a given size a is accepted if the inequality Y2 a 2 Y Y2 1-a 2 holds where Yz a is the a-quantile of the statistic y The values of Yi a for various n and a can be found in statistical tables. . Comparison of expectations of two normal populations. Suppose that X .