SUBROUTINE cdff(which,p,q,f,dfn,dfd,status,bound) C********************************************************************** C C SUBROUTINE CDFF( WHICH, P, Q, F, DFN, DFD, STATUS, BOUND ) C Cumulative Distribution Function C F distribution C C C Function C C C Calculates any one parameter of the F distribution C given values for the others. C C C Arguments C C C WHICH --> Integer indicating which of the next four argument C values is to be calculated from the others. C Legal range: 1..4 C iwhich = 1 : Calculate P and Q from F,DFN and DFD C iwhich = 2 : Calculate F from P,Q,DFN and DFD C iwhich = 3 : Calculate DFN from P,Q,F and DFD C iwhich = 4 : Calculate DFD from P,Q,F and DFN C INTEGER WHICH C C P <--> The integral from 0 to F of the f-density. C Input range: [0,1]. C DOUBLE PRECISION P C C Q <--> 1-P. C Input range: (0, 1]. C P + Q = 1.0. C DOUBLE PRECISION Q C C F <--> Upper limit of integration of the f-density. C Input range: [0, +infinity). C Search range: [0,1E100] C DOUBLE PRECISION F C C DFN < --> Degrees of freedom of the numerator sum of squares. C Input range: (0, +infinity). C Search range: [ 1E-100, 1E100] C DOUBLE PRECISION DFN C C DFD < --> Degrees of freedom of the denominator sum of squares. C Input range: (0, +infinity). C Search range: [ 1E-100, 1E100] C DOUBLE PRECISION DFD C C STATUS <-- 0 if calculation completed correctly C -I if input parameter number I is out of range C 1 if answer appears to be lower than lowest C search bound C 2 if answer appears to be higher than greatest C search bound C 3 if P + Q .ne. 1 C INTEGER STATUS C C BOUND <-- Undefined if STATUS is 0 C C Bound exceeded by parameter number I if STATUS C is negative. C C Lower search bound if STATUS is 1. C C Upper search bound if STATUS is 2. C C C Method C C C Formula 26.6.2 of Abramowitz and Stegun, Handbook of C Mathematical Functions (1966) is used to reduce the computation C of the cumulative distribution function for the F variate to C that of an incomplete beta. C C Computation of other parameters involve a search for a value that C produces the desired value of P. The search relies on the C monotinicity of P with the other parameter. C C WARNING C C The value of the cumulative F distribution is not necessarily C monotone in either degrees of freedom. There thus may be two C values that provide a given CDF value. This routine assumes C monotonicity and will find an arbitrary one of the two values. C C********************************************************************** C .. Parameters .. DOUBLE PRECISION tol PARAMETER (tol=1.0D-8) DOUBLE PRECISION atol PARAMETER (atol=1.0D-50) DOUBLE PRECISION zero,inf PARAMETER (zero=1.0D-100,inf=1.0D100) C .. C .. Scalar Arguments .. DOUBLE PRECISION bound,dfd,dfn,f,p,q INTEGER status,which C .. C .. Local Scalars .. DOUBLE PRECISION ccum,cum,fx,pq LOGICAL qhi,qleft,qporq C .. C .. External Functions .. DOUBLE PRECISION spmpar EXTERNAL spmpar C .. C .. External Subroutines .. EXTERNAL cumf,dinvr,dstinv C .. C .. Intrinsic Functions .. INTRINSIC abs C .. IF (.NOT. ((which.LT.1).OR. (which.GT.4))) GO TO 30 IF (.NOT. (which.LT.1)) GO TO 10 bound = 1.0D0 GO TO 20 10 bound = 4.0D0 20 status = -1 RETURN 30 IF (which.EQ.1) GO TO 70 IF (.NOT. ((p.LT.0.0D0).OR. (p.GT.1.0D0))) GO TO 60 IF (.NOT. (p.LT.0.0D0)) GO TO 40 bound = 0.0D0 GO TO 50 40 bound = 1.0D0 50 status = -2 RETURN 60 CONTINUE 70 IF (which.EQ.1) GO TO 110 IF (.NOT. ((q.LE.0.0D0).OR. (q.GT.1.0D0))) GO TO 100 IF (.NOT. (q.LE.0.0D0)) GO TO 80 bound = 0.0D0 GO TO 90 80 bound = 1.0D0 90 status = -3 RETURN 100 CONTINUE 110 IF (which.EQ.2) GO TO 130 IF (.NOT. (f.LT.0.0D0)) GO TO 120 bound = 0.0D0 status = -4 RETURN 120 CONTINUE 130 IF (which.EQ.3) GO TO 150 IF (.NOT. (dfn.LE.0.0D0)) GO TO 140 bound = 0.0D0 status = -5 RETURN 140 CONTINUE 150 IF (which.EQ.4) GO TO 170 IF (.NOT. (dfd.LE.0.0D0)) GO TO 160 bound = 0.0D0 status = -6 RETURN 160 CONTINUE 170 IF (which.EQ.1) GO TO 210 pq = p + q IF (.NOT. (abs(((pq)-0.5D0)-0.5D0).GT. + (3.0D0*spmpar(1)))) GO TO 200 IF (.NOT. (pq.LT.0.0D0)) GO TO 180 bound = 0.0D0 GO TO 190 180 bound = 1.0D0 190 status = 3 RETURN 200 CONTINUE 210 IF (.NOT. (which.EQ.1)) qporq = p .LE. q IF ((1).EQ. (which)) THEN CALL cumf(f,dfn,dfd,p,q) status = 0 ELSE IF ((2).EQ. (which)) THEN f = 5.0D0 CALL dstinv(0.0D0,inf,0.5D0,0.5D0,5.0D0,atol,tol) status = 0 CALL dinvr(status,f,fx,qleft,qhi) 220 IF (.NOT. (status.EQ.1)) GO TO 250 CALL cumf(f,dfn,dfd,cum,ccum) IF (.NOT. (qporq)) GO TO 230 fx = cum - p GO TO 240 230 fx = ccum - q 240 CALL dinvr(status,f,fx,qleft,qhi) GO TO 220 250 IF (.NOT. (status.EQ.-1)) GO TO 280 IF (.NOT. (qleft)) GO TO 260 status = 1 bound = 0.0D0 GO TO 270 260 status = 2 bound = inf 270 CONTINUE 280 CONTINUE ELSE IF ((3).EQ. (which)) THEN dfn = 5.0D0 CALL dstinv(zero,inf,0.5D0,0.5D0,5.0D0,atol,tol) status = 0 CALL dinvr(status,dfn,fx,qleft,qhi) 290 IF (.NOT. (status.EQ.1)) GO TO 320 CALL cumf(f,dfn,dfd,cum,ccum) IF (.NOT. (qporq)) GO TO 300 fx = cum - p GO TO 310 300 fx = ccum - q 310 CALL dinvr(status,dfn,fx,qleft,qhi) GO TO 290 320 IF (.NOT. (status.EQ.-1)) GO TO 350 IF (.NOT. (qleft)) GO TO 330 status = 1 bound = zero GO TO 340 330 status = 2 bound = inf 340 CONTINUE 350 CONTINUE ELSE IF ((4).EQ. (which)) THEN dfd = 5.0D0 CALL dstinv(zero,inf,0.5D0,0.5D0,5.0D0,atol,tol) status = 0 CALL dinvr(status,dfd,fx,qleft,qhi) 360 IF (.NOT. (status.EQ.1)) GO TO 390 CALL cumf(f,dfn,dfd,cum,ccum) IF (.NOT. (qporq)) GO TO 370 fx = cum - p GO TO 380 370 fx = ccum - q 380 CALL dinvr(status,dfd,fx,qleft,qhi) GO TO 360 390 IF (.NOT. (status.EQ.-1)) GO TO 420 IF (.NOT. (qleft)) GO TO 400 status = 1 bound = zero GO TO 410 400 status = 2 bound = inf 410 CONTINUE 420 END IF RETURN END