SUBROUTINE NORPPF(P,PPF) C C PURPOSE--THIS SUBROUTINE COMPUTES THE PERCENT POINT C FUNCTION VALUE FOR THE NORMAL (GAUSSIAN) C DISTRIBUTION WITH MEAN = 0 AND STANDARD DEVIATION = 1. C THIS DISTRIBUTION IS DEFINED FOR ALL X AND HAS C THE PROBABILITY DENSITY FUNCTION C F(X) = (1/SQRT(2*PI))*EXP(-X*X/2). C NOTE THAT THE PERCENT POINT FUNCTION OF A DISTRIBUTION C IS IDENTICALLY THE SAME AS THE INVERSE CUMULATIVE C DISTRIBUTION FUNCTION OF THE DISTRIBUTION. C INPUT ARGUMENTS--P = THE SINGLE PRECISION VALUE C (BETWEEN 0.0 AND 1.0) C AT WHICH THE PERCENT POINT C FUNCTION IS TO BE EVALUATED. C OUTPUT ARGUMENTS--PPF = THE SINGLE PRECISION PERCENT C POINT FUNCTION VALUE. C OUTPUT--THE SINGLE PRECISION PERCENT POINT C FUNCTION VALUE PPF. C PRINTING--NONE UNLESS AN INPUT ARGUMENT ERROR CONDITION EXISTS. C RESTRICTIONS--P SHOULD BE BETWEEN 0.0 AND 1.0, EXCLUSIVELY. C OTHER DATAPAC SUBROUTINES NEEDED--NONE. C FORTRAN LIBRARY SUBROUTINES NEEDED--SQRT, ALOG. C MODE OF INTERNAL OPERATIONS--SINGLE PRECISION. C LANGUAGE--ANSI FORTRAN. C REFERENCES--ODEH AND EVANS, THE PERCENTAGE POINTS C OF THE NORMAL DISTRIBUTION, ALGORTIHM 70, C APPLIED STATISTICS, 1974, PAGES 96-97. C --EVANS, ALGORITHMS FOR MINIMAL DEGREE C POLYNOMIAL AND RATIONAL APPROXIMATION, C M. SC. THESIS, 1972, UNIVERSITY C OF VICTORIA, B. C., CANADA. C --HASTINGS, APPROXIMATIONS FOR DIGITAL C COMPUTERS, 1955, PAGES 113, 191, 192. C --NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS C SERIES 55, 1964, PAGE 933, FORMULA 26.2.23. C --FILLIBEN, SIMPLE AND ROBUST LINEAR ESTIMATION C OF THE LOCATION PARAMETER OF A SYMMETRIC C DISTRIBUTION (UNPUBLISHED PH.D. DISSERTATION, C PRINCETON UNIVERSITY), 1969, PAGES 21-44, 229-231. C --FILLIBEN, 'THE PERCENT POINT FUNCTION', C (UNPUBLISHED MANUSCRIPT), 1970, PAGES 28-31. C --JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE C DISTRIBUTIONS--1, 1970, PAGES 40-111. C --THE KELLEY STATISTICAL TABLES, 1948. C --OWEN, HANDBOOK OF STATISTICAL TABLES, C 1962, PAGES 3-16. C --PEARSON AND HARTLEY, BIOMETRIKA TABLES C FOR STATISTICIANS, VOLUME 1, 1954, C PAGES 104-113. C COMMENTS--THE CODING AS PRESENTED BELOW C IS ESSENTIALLY IDENTICAL TO THAT C PRESENTED BY ODEH AND EVANS C AS ALGORTIHM 70 OF APPLIED STATISTICS. C THE PRESENT AUTHOR HAS MODIFIED THE C ORIGINAL ODEH AND EVANS CODE WITH ONLY C MINOR STYLISTIC CHANGES. C --AS POINTED OUT BY ODEH AND EVANS C IN APPLIED STATISTICS, C THEIR ALGORITHM REPRESENTES A C SUBSTANTIAL IMPROVEMENT OVER THE C PREVIOUSLY EMPLOYED C HASTINGS APPROXIMATION FOR THE C NORMAL PERCENT POINT FUNCTION-- C THE ACCURACY OF APPROXIMATION C BEING IMPROVED FROM 4.5*(10**-4) C TO 1.5*(10**-8). 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--JUNE 1972. C UPDATED --SEPTEMBER 1975. C UPDATED --NOVEMBER 1975. C UPDATED --OCTOBER 1976. C C--------------------------------------------------------------------- C DATA P0,P1,P2,P3,P4 1/-.322232431088,-1.0, 1 -.342242088547,-.204231210245E-1, 1 -.453642210148E-4/ DATA Q0,Q1,Q2,Q3,Q4 1/.993484626060E-1,.588581570495, 1 .531103462366,.103537752850, 1 .38560700634E-2/ C IPR=6 C C CHECK THE INPUT ARGUMENTS FOR ERRORS C IF(P.LE.0.0.OR.P.GE.1.0)GOTO50 GOTO90 50 WRITE(IPR,1) WRITE(IPR,46)P RETURN 90 CONTINUE 1 FORMAT(1H ,115H***** FATAL ERROR--THE FIRST INPUT ARGUMENT TO THE 1 NORPPF SUBROUTINE IS OUTSIDE THE ALLOWABLE (0,1) INTERVAL *****) 46 FORMAT(1H , 35H***** THE VALUE OF THE ARGUMENT IS ,E15.8,6H *****) C C-----START POINT----------------------------------------------------- C IF(P.NE.0.5)GOTO150 PPF=0.0 RETURN C 150 R=P IF(P.GT.0.5)R=1.0-R T=SQRT(-2.0*ALOG(R)) ANUM=((((T*P4+P3)*T+P2)*T+P1)*T+P0) ADEN=((((T*Q4+Q3)*T+Q2)*T+Q1)*T+Q0) PPF=T+(ANUM/ADEN) IF(P.LT.0.5)PPF=-PPF RETURN C END