KS Q ISO 5479-2009 Statistical interpretation of data－Tests for departure from the normal distribution《数据的统计解释 偏离正态分布的检验》.pdf

1、 KSKSKSKSKSKSKSK KSKSKS KSKSK KSKS KSK KS KS Q ISO 5479 KS Q ISO 5479:2009 2009 12 15 http:/www.kats.go.krKS Q ISO 5479:2009 : ( ) ( ) ( ) : (http:/www.standard.go.kr) ： ：2006 10 19 ：2009 12 15 2009-0818 ： ： ( 02-509-7230) (http:/www.kats.go.kr). 10 5 , . KS Q ISO 5479:2009 Statistical interpretatio

2、n of data Tests for departure from the normal distribution 1997 1 ISO 5479, Statistical interpretation of data Tests for departure from the normal distribution , . 1 1.1 , . 1.2 . ( , ), . , t . 1.3 . ( , ) . 1.4 . . 1.5 . 1.6 8 . 8 . 2 . . ( ) . KS Q ISO 3534 1： 2009, 1： KS Q ISO 5479:2009 2 3 3.1

3、KS Q ISO 3534 1 . 3.2 akShapiro Wilk A Epps Pulley b2 (kurtosis) 1b (skewness) B Epps Pulley E Gj h H0 H1 k x mj j n p p P PkX(k) S Shapiro Wilk T TEPEpps Pulley up p vj W Shapiro Wilk Wj x X X x(j) j x(k) k x 2 2 2 3 1 (n) (n) KS Q ISO 5479:2009 3 (n) 2 3 3 4 4 (2= ) 4 4.1 . , , . . 4.2 . , . 5. .

4、. . . 4.3 n . T . T . 4.4 T . T P . ( 1 ). ( ) ( ) . 4.5 . ( 2 ) . ( , ) . , . 4.6 . . . . KS Q ISO 5479:2009 4 . , , . . 4.7 . , , . . (non-null) . 4.8 8 14 9 , 0.05 0.01 . . 0.05 0.01 . 4.9 . , . 5 5.1 . ( ) . X . X . . X , , . 1 . , . A . , . . . ( , 5 6 ) . ( , 7 ) , . KS Q ISO 5479:2009 5 . , .

5、 5.2 x(1), x(2), L, x(n) x(k) (1) . Pk (k 3/8)/(n 1/4) (1) 1 (1) Pk (k 1/2)n Pk k/(n 1) . FE(X(k) , . 5.3 2 . 1 , % KS Q ISO 5479:2009 6 2 b)a)KS Q ISO 5479:2009 7 1 15 x(k) . 1 15 - x(k) lg10 x(k) k 4/18/3+=nkP x(k)lg10x(k) 1 0.041 0.200 0.301 2 0.107 0.330 0.519 3 0.172 0.445 0.648 4 0.238 0.490 0

6、.690 5 0.303 0.780 0.892 6 0.369 0.920 0.964 7 0.434 0.950 0.978 8 0.500 0.970 0.987 9 0.566 1.040 1.017 10 0.631 1.710 1.233 11 0.697 2.220 1.346 12 0.762 2.275 1.357 13 0.828 3.650 1.562 14 0.893 7.000 1.845 15 0.959 8.800 1.944 2 1 . . Pk (k 3/8)/(n 1/4) k x(k) 2 a) . . x(k) lg10x(k) 2(b) . . 5.4

7、 . . . , y log x y x 2(b) 5 . 3 7 . 3 4 (platykurtic) (leptokurtic) . KS Q ISO 5479:2009 8 5 6 . 7 . 3 4 , % , % KS Q ISO 5479:2009 9 5 6 , % , % KS Q ISO 5479:2009 10 7 6 6.1 6.1.1 . E(X) X 3 0)(33= XE (2) . 3 0333/22331= =XE (3) 4 23/224= (4) )(22= XE (5) , % KS Q ISO 5479:2009 11 )(44= XE (6) 1 0

8、 , . 2 . 2 3 . 2(1 )2 1 . 6.1.2 H1： 3 0 01 ( 5 ). H1： 3 0 01H 2 . x (1.25 1.35L 5.10)/50 2.873 m2 (1.25 2.873)2L (5.10 2.873)2/50 0.937 921 m3 (1.25 2.873)3L (5.10 2.873)3/50 0.254 559 280.02/3231=mmb 0.05, p 1 0.95 n 50 0.53( 8 KS Q ISO 5479:2009 13 ). 1b . . 2 1.25 2.05 2.60 3.10 4.00 1.35 2.10 2.

9、60 3.15 4.00 1.40 2.15 2.70 3.15 4.05 1.50 2.15 2.75 3.20 4.05 1.55 2.15 2.75 3.30 4.10 1.60 2.20 2.80 3.45 4.20 1.75 2.25 2.95 3.50 4.45 1.75 2.35 2.95 3.50 4.50 1.85 2.40 3.00 3.80 4.70 1.95 2.55 3.05 3.90 5.10 50 6.3 b2 n8 . 9 n5 000 . (kurtosis in excess) H1： 2 3 b2 p 1 0.95 p 1 0.99 n , 0.05 0.

10、01 . (kurtosis in default) H1： 2 3 b2 p 0.05 p 0.01 n , 0.05 0.01 . 9 p 0.01, 0.05, 0.95 0.99 n 8(1)10,12,15(5)50(25)150(50)1 000(200)2 000(500)5 000 b2 . 2 b2 . 3 50 . . 2 3 . H1： 2 3 KS Q ISO 5479:2009 14 3 50 9.5 5.1 5.7 16.6 12.9 14.4 5.8 10.8 20.9 13.3 10.2 9.2 22.5 21.5 8.5 4.2 12.9 5.5 9.1 3.

11、3 17.1 6.3 8.6 11.9 1.4 4.4 3.1 7.4 12.9 12.9 4.5 12.9 6.9 26.6 16.3 8.5 11.9 7.9 7.5 15.6 9.9 11.4 3.6 5.4 11.4 7.7 5.9 7.3 32.0 6.0 3 . x (9.5 14.4L 6.0)/50 10.542 m2 (9.5 10.542)2L (6.0 10.542)2/50 37.996 4 m4 (9.5 10.542)4L (6.10 10.542)4/50 7 098.04 b2224mm 4.916 0.05, p 1 0.95 n 50 3.99( 9 ).

12、b2 4.916 0.05 . . 0.01 4.88 . . 7 1b b2 ( ) 20n1 000 . 7.1 0 0:11bH / 23 01 2 3 1 0 23 01 23 . KS Q ISO 5479:2009 15 01 2 3 . . . 7.2 6.1.6 (9) (10) |1b b2 . |1b b2 (0, 3) ( |1b , b2) p . n 20(5)65(10)85,100,120,150(50)300, 500,1 000 (p 0.95) 9 a) , (p 0.99) 9 b) . 1 p n . 3 1b b2 2 . 3 . m3 (9.5 10

13、.542)3L (6.0 10.542)3/50 308.106 315.1/2/3231= mmb ( |1b 1.315, b2 4.916) 0.01 9 b) n 50 . . . 8 8.1 8.1.1 , . 8.1.2 (omnibus) . Shapiro Wilk Epps Pulley . Shapiro Wilk ( , |1 1/2 2 3) ( , |1 1/2) , Epps Pulley . 8.2 Shapiro Wilk 8n50 . n 8 . Shapiro Wilk . . KS Q ISO 5479:2009 16 . . 5.3 n x(1), x(

14、2), L, x(n) , S . =+)()1( kknkxxaS (11) k n 1 n/2 1 (n 1)/2 , ak n . ak 10 W S2/(nm2) (12) nm22)( xxi , . p p p . 11 p 0.01 p 0.05 W p . 4 Shapiro Wilk . 4 44 . x(k), x(n 1 k) x(n 1 k) x(k) . 4 . = 114.78544/5453444/)(kxx = 8726302)(2xxnmk 10 n 44 ak 4 . =+=+263.78792004.05007266.05542387.0)()1(Lkkn

15、kxxaS 982.043.872630/)7262.787(222=nmSW 11 n 44 p 0.05 p 0.944 . W 0.05 . KS Q ISO 5479:2009 17 4 k x(k) x(n 1 k)x(n 1 k)x(k)ak1 520 1 074 554 0.387 2 2 556 1 056 500 0.266 7 3 561 963 402 0.232 3 4 616 952 336 0.207 2 5 635 926 291 0.186 8 6 669 922 253 0.169 5 7 686 904 218 0.154 2 8 692 900 208 0.140 5 9 704 889 185 0.127 8 10 707 879 172 0.116 0 11 711 873 162 0.104 9 12 713 862 149 0.094 3 13 714 851 137 0.084 2 14 719