C KLM2 10
C ..................................................................KLM2 20
C KLM2 30
C SUBROUTINE KOLM2 KLM2 40
C KLM2 50
C PURPOSE KLM2 60
C KLM2 70
C TESTS THE DIFFERENCE BETWEEN TWO SAMPLE DISTRIBUTION KLM2 80
C FUNCTIONS USING THE KOLMOGOROV-SMIRNOV TEST KLM2 90
C KLM2 100
C USAGE KLM2 110
C CALL KOLM2(X,Y,N,M,Z,PROB) KLM2 120
C KLM2 130
C DESCRIPTION OF PARAMETERS KLM2 140
C X - INPUT VECTOR OF N INDEPENDENT OBSERVATIONS. ON KLM2 150
C RETURN FROM KOLM2, X HAS BEEN SORTED INTO A KLM2 160
C MONOTONIC NON-DECREASING SEQUENCE. KLM2 170
C Y - INPUT VECTOR OF M INDEPENDENT OBSERVATIONS. ON KLM2 180
C RETURN FROM KOLM2, Y HAS BEEN SORTED INTO A KLM2 190
C MONOTONIC NON-DECREASING SEQUENCE. KLM2 200
C N - NUMBER OF OBSERVATIONS IN X KLM2 210
C M - NUMBER OF OBSERVATIONS IN Y KLM2 220
C Z - OUTPUT VARIABLE CONTAINING THE GREATEST VALUE WITH KLM2 230
C RESPECT TO THE SPECTRUM OF X AND Y OF KLM2 240
C SQRT((M*N)/(M+N))*ABS(FN(X)-GM(Y)) WHERE KLM2 250
C FN(X) IS THE EMPIRICAL DISTRIBUTION FUNCTION OF THE KLM2 260
C SET (X) AND GM(Y) IS THE EMPIRICAL DISTRIBUTION KLM2 270
C FUNCTION OF THE SET (Y). KLM2 280
C PROB - OUTPUT VARIABLE CONTAINING THE PROBABILITY OF KLM2 290
C THE STATISTIC BEING GREATER THAN OR EQUAL TO Z IF KLM2 300
C THE HYPOTHESIS THAT X AND Y ARE FROM THE SAME PDF IS KLM2 310
C TRUE. E.G., PROB= 0.05 IMPLIES THAT ONE CAN REJECT KLM2 320
C THE NULL HYPOTHESIS THAT THE SETS X AND Y ARE FROM KLM2 330
C THE SAME DENSITY WITH 5 PER CENT PROBABILITY OF BEINGKLM2 340
C INCORRECT. PROB = 1. - SMIRN(Z). KLM2 350
C KLM2 360
C REMARKS KLM2 370
C N AND M SHOULD BE GREATER THAN OR EQUAL TO 100. (SEE THE KLM2 380
C MATHEMATICAL DESCRIPTION FOR THIS SUBROUTINE AND FOR THE KLM2 390
C SUBROUTINE SMIRN, CONCERNING ASYMPTOTIC FORMULAE). KLM2 400
C KLM2 410
C DOUBLE PRECISION USAGE---IT IS DOUBTFUL THAT THE USER WILL KLM2 420
C WISH TO PERFORM THIS TEST USING DOUBLE PRECISION ACCURACY. KLM2 430
C IF ONE WISHES TO COMMUNICATE WITH KOLM2 IN A DOUBLE KLM2 440
C PRECISION PROGRAM, HE SHOULD CALL THE FORTRAN SUPPLIED KLM2 450
C PROGRAM SNGL(X) PRIOR TO CALLING KOLM2, AND CALL THE KLM2 460
C FORTRAN SUPPLIED PROGRAM DBLE(X) AFTER EXITING FROM KOLM2. KLM2 470
C (NOTE THAT SUBROUTINE SMIRN DOES HAVE DOUBLE PRECISION KLM2 480
C CAPABILITY AS SUPPLIED BY THIS PACKAGE.) KLM2 490
C KLM2 500
C KLM2 510
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED KLM2 520
C SMIRN KLM2 530
C KLM2 540
C METHOD KLM2 550
C FOR REFERENCE, SEE (1) W. FELLER--ON THE KOLMOGOROV-SMIRNOV KLM2 560
C LIMIT THEOREMS FOR EMPIRICAL DISTRIBUTIONS-- KLM2 570
C ANNALS OF MATH. STAT., 19, 1948. 177-189, KLM2 580
C (2) N. SMIRNOV--TABLE FOR ESTIMATING THE GOODNESS OF FIT KLM2 590
C OF EMPIRICAL DISTRIBUTIONS--ANNALS OF MATH. STAT., 19, KLM2 600
C 1948. 279-281. KLM2 610
C (3) R. VON MISES--MATHEMATICAL THEORY OF PROBABILITY AND KLM2 620
C STATISTICS--ACADEMIC PRESS, NEW YORK, 1964. 490-493, KLM2 630
C (4) B.V. GNEDENKO--THE THEORY OF PROBABILITY--CHELSEA KLM2 640
C PUBLISHING COMPANY, NEW YORK, 1962. 384-401. KLM2 650
C KLM2 660
C ..................................................................KLM2 670
C KLM2 680
SUBROUTINE KOLM2(X,Y,N,M,Z,PROB) KLM2 690
DIMENSION X(1),Y(1) KLM2 700
C KLM2 710
C SORT X INTO ASCENDING SEQUENCE KLM2 720
C KLM2 730
DO 5 I=2,N KLM2 740
IF(X(I)-X(I-1))1,5,5 KLM2 750
1 TEMP=X(I) KLM2 760
IM=I-1 KLM2 770
DO 3 J=1,IM KLM2 780
L=I-J KLM2 790
IF(TEMP-X(L))2,4,4 KLM2 800
2 X(L+1)=X(L) KLM2 810
3 CONTINUE KLM2 820
X(1)=TEMP KLM2 830
GO TO 5 KLM2 840
4 X(L+1)=TEMP KLM2 850
5 CONTINUE KLM2 860
C KLM2 870
C SORT Y INTO ASCENDING SEQUENCE KLM2 880
C KLM2 890
DO 10 I=2,M KLM2 900
IF(Y(I)-Y(I-1))6,10,10 KLM2 910
6 TEMP=Y(I) KLM2 920
IM=I-1 KLM2 930
DO 8 J=1,IM KLM2 940
L=I-J KLM2 950
IF(TEMP-Y(L))7,9,9 KLM2 960
7 Y(L+1)=Y(L) KLM2 970
8 CONTINUE KLM2 980
Y(1)=TEMP KLM2 990
GO TO 10 KLM21000
9 Y(L+1)=TEMP KLM21010
10 CONTINUE KLM21020
C KLM21030
C CALCULATE D = ABS(FN-GM) OVER THE SPECTRUM OF X AND Y KLM21040
C KLM21050
XN=FLOAT(N) KLM21060
XN1=1./XN KLM21070
XM=FLOAT(M) KLM21080
XM1=1./XM KLM21090
D=0.0 KLM21100
I=0 KLM21110
J=0 KLM21120
K=0 KLM21130
L=0 KLM21140
11 IF(X(I+1)-Y(J+1))12,13,18 KLM21150
12 K=1 KLM21160
GO TO 14 KLM21170
13 K=0 KLM21180
14 I=I+1 KLM21190
IF(I-N)15,21,21 KLM21200
15 IF(X(I+1)-X(I))14,14,16 KLM21210
16 IF(K)17,18,17 KLM21220
C KLM21230
C CHOOSE THE MAXIMUM DIFFERENCE, D KLM21240
C KLM21250
17 D=AMAX1(D,ABS(FLOAT(I)*XN1-FLOAT(J)*XM1)) KLM21260
IF(L)22,11,22 KLM21270
18 J=J+1 KLM21280
IF(J-M)19,20,20 KLM21290
19 IF(Y(J+1)-Y(J))18,18,17 KLM21300
20 L=1 KLM21310
GO TO 17 KLM21320
21 L=1 KLM21330
GO TO 16 KLM21340
C KLM21350
C CALCULATE THE STATISTIC Z KLM21360
C KLM21370
22 Z=D*SQRT((XN*XM)/(XN+XM)) KLM21380
C KLM21390
C CALCULATE THE PROBABILITY ASSOCIATED WITH Z KLM21400
C KLM21410
CALL SMIRN(Z,PROB) KLM21420
PROB=1.0-PROB KLM21430
RETURN KLM21440
END KLM21450