SUBROUTINE TPLT(X,N,NU) C C PURPOSE--THIS SUBROUTINE GENERATES A STUDENT'S T C PROBABILITY PLOT (WITH INTEGER C DEGREES OF FREEDOM PARAMETER VALUE = NU). C THE PROTOTYPE STUDENT'S T DISTRIBUTION USED C HEREIN IS DEFINED FOR ALL X, C AND ITS PROBABILITY DENSITY FUNCTION IS GIVEN C IN THE REFERENCES BELOW. C AS USED HEREIN, A PROBABILITY PLOT FOR A DISTRIBUTION C IS A PLOT OF THE ORDERED OBSERVATIONS VERSUS C THE ORDER STATISTIC MEDIANS FOR THAT DISTRIBUTION. C THE STUDENT'S T PROBABILITY PLOT IS USEFUL IN C GRAPHICALLY TESTING THE COMPOSITE (THAT IS, C LOCATION AND SCALE PARAMETERS NEED NOT BE SPECIFIED) C HYPOTHESIS THAT THE UNDERLYING DISTRIBUTION C FROM WHICH THE DATA HAVE BEEN RANDOMLY DRAWN C IS THE STUDENT'S T DISTRIBUTION C WITH DEGREES OF FREEDOM PARAMETER VALUE = NU. C IF THE HYPOTHESIS IS TRUE, THE PROBABILITY PLOT C SHOULD BE NEAR-LINEAR. C A MEASURE OF SUCH LINEARITY IS GIVEN BY THE C CALCULATED PROBABILITY PLOT CORRELATION COEFFICIENT. C INPUT ARGUMENTS--X = THE SINGLE PRECISION VECTOR OF C (UNSORTED OR SORTED) OBSERVATIONS. C --N = THE INTEGER NUMBER OF OBSERVATIONS C IN THE VECTOR X. C --NU = THE INTEGER NUMBER OF DEGREES C OF FREEDOM. C NU SHOULD BE POSITIVE. C OUTPUT--A ONE-PAGE STUDENT'S T PROBABILITY PLOT. C PRINTING--YES. C RESTRICTIONS--THE MAXIMUM ALLOWABLE VALUE OF N C FOR THIS SUBROUTINE IS 7500. C --NU SHOULD BE POSITIVE. C OTHER DATAPAC SUBROUTINES NEEDED--SORT, UNIMED, TPPF, NORPPF, C PLOT. C FORTRAN LIBRARY SUBROUTINES NEEDED--SQRT. C MODE OF INTERNAL OPERATIONS--SINGLE PRECISION. C LANGUAGE--ANSI FORTRAN. C REFERENCES--FILLIBEN, 'TECHNIQUES FOR TAIL LENGTH ANALYSIS', C PROCEEDINGS OF THE EIGHTEENTH CONFERENCE C ON THE DESIGN OF EXPERIMENTS IN ARMY RESEARCH C DEVELOPMENT AND TESTING (ABERDEEN, MARYLAND, C OCTOBER, 1972), PAGES 425-450. C --HAHN AND SHAPIRO, STATISTICAL METHODS IN ENGINEERING, C 1967, PAGES 260-308. C --NATIONAL BUREAU OF STANDARDS APPLIED MATHMATICS C SERIES 55, 1964, PAGE 949, FORMULA 26.7.5. C --JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE C DISTRIBUTIONS--2, 1970, PAGE 102, C FORMULA 11. C --FEDERIGHI, 'EXTENDED TABLES OF THE C PERCENTAGE POINTS OF STUDENT'S T C DISTRIBUTION, JOURNAL OF THE C AMERICAN STATISTICAL ASSOCIATION, C 1969, PAGES 683-688. C --HASTINGS AND PEACOCK, STATISTICAL C DISTRIBUTIONS--A HANDBOOK FOR C STUDENTS AND PRACTITIONERS, 1975, C PAGES 120-123. C WRITTEN BY--JAMES J. FILLIBEN C STATISTICAL ENGINEERING LABORATORY (205.03) C NATIONAL BUREAU OF STANDARDS C WASHINGTON, D. C. 20234 C PHONE: 301-921-2315 C ORIGINAL VERSION--NOVEMBER 1975. C UPDATED --FEBRUARY 1976. C UPDATED --FEBRUARY 1977. C C--------------------------------------------------------------------- C DIMENSION X(1) DIMENSION Y(7500),W(7500) COMMON /BLOCK2/ WS(15000) EQUIVALENCE (Y(1),WS(1)),(W(1),WS(7501)) C IPR=6 IUPPER=7500 C C CHECK THE INPUT ARGUMENTS FOR ERRORS C IF(N.LT.1.OR.N.GT.IUPPER)GOTO50 IF(N.EQ.1)GOTO55 IF(NU.LE.0)GOTO60 HOLD=X(1) DO65I=2,N IF(X(I).NE.HOLD)GOTO90 65 CONTINUE WRITE(IPR, 9)HOLD RETURN 50 WRITE(IPR,17)IUPPER WRITE(IPR,47)N RETURN 55 WRITE(IPR,18) RETURN 60 WRITE(IPR,25) WRITE(IPR,47)NU RETURN 90 CONTINUE 9 FORMAT(1H ,109H***** NON-FATAL DIAGNOSTIC--THE FIRST INPUT ARGUME 1NT (A VECTOR) TO THE TPLT SUBROUTINE HAS ALL ELEMENTS = ,E15.8,6 1H *****) 17 FORMAT(1H , 98H***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE 1 TPLT SUBROUTINE IS OUTSIDE THE ALLOWABLE (1,,I6,16H) INTERVAL * 1****) 18 FORMAT(1H ,100H***** NON-FATAL DIAGNOSTIC--THE SECOND INPUT ARGUME 1NT TO THE TPLT SUBROUTINE HAS THE VALUE 1 *****) 25 FORMAT(1H , 91H***** FATAL ERROR--THE THIRD INPUT ARGUMENT TO THE 1 TPLT SUBROUTINE IS NON-POSITIVE *****) 47 FORMAT(1H , 35H***** THE VALUE OF THE ARGUMENT IS ,I8 ,6H *****) C C-----START POINT----------------------------------------------------- C AN=N C C SORT THE DATA C CALL SORT(X,N,Y) C C GENERATE UNIFORM ORDER STATISTIC MEDIANS C CALL UNIMED(N,W) C C COMPUTE STUDENT'S T DISTRIBUTION ORDER STATISTIC MEDIANS C DO100I=1,N CALL TPPF(W(I),NU,W(I)) 100 CONTINUE C C PLOT THE ORDERED OBSERVATIONS VERSUS ORDER STATISTICS MEDIANS. C COMPUTE THE TAIL LENGTH MEASURE OF THE DISTRIBUTION. C WRITE OUT THE TAIL LENGTH MEASURE OF THE DISTRIBUTION C AND THE SAMPLE SIZE. C CALL PLOT(Y,W,N) Q=.9975 CALL TPPF(Q,NU,PP9975) Q=.0025 CALL TPPF(Q,NU,PP0025) Q=.975 CALL TPPF(Q,NU,PP975) Q=.025 CALL TPPF(Q,NU,PP025) TAU=(PP9975-PP0025)/(PP975-PP025) WRITE(IPR,105)NU,TAU,N C C COMPUTE THE PROBABILITY PLOT CORRELATION COEFFICIENT. C COMPUTE LOCATION AND SCALE ESTIMATES C FROM THE INTERCEPT AND SLOPE OF THE PROBABILITY PLOT. C THEN WRITE THEM OUT. C SUM1=0.0 SUM2=0.0 DO200I=1,N SUM1=SUM1+Y(I) SUM2=SUM2+W(I) 200 CONTINUE YBAR=SUM1/AN WBAR=SUM2/AN SUM1=0.0 SUM2=0.0 SUM3=0.0 DO300I=1,N SUM1=SUM1+(Y(I)-YBAR)*(Y(I)-YBAR) SUM2=SUM2+(Y(I)-YBAR)*(W(I)-WBAR) SUM3=SUM3+(W(I)-WBAR)*(W(I)-WBAR) 300 CONTINUE CC=SUM2/SQRT(SUM3*SUM1) YSLOPE=SUM2/SUM3 YINT=YBAR-YSLOPE*WBAR WRITE(IPR,305)CC,YINT,YSLOPE C 105 FORMAT(1H ,55HSTUDENT'S T PROBABILITY PLOT WITH DEGREES OF FREEDOM 1 = ,I8,1X,7H(TAU = ,E15.8,1H),11X,20HTHE SAMPLE SIZE N = ,I7) 305 FORMAT(1H ,43HPROBABILITY PLOT CORRELATION COEFFICIENT = ,F8.5,5X, 122HESTIMATED INTERCEPT = ,E15.8,3X,18HESTIMATED SLOPE = ,E15.8) C RETURN END