SUBROUTINE cdffnc(which,p,q,f,dfn,dfd,phonc,status,bound) C********************************************************************** C C SUBROUTINE CDFFNC( WHICH, P, Q, F, DFN, DFD, PNONC, STATUS, BOUND ) C Cumulative Distribution Function C Non-central F distribution C C C Function C C C Calculates any one parameter of the Non-central F C distribution given values for the others. C C C Arguments C C C WHICH --> Integer indicating which of the next five argument C values is to be calculated from the others. C Legal range: 1..5 C iwhich = 1 : Calculate P and Q from F,DFN,DFD and PNONC C iwhich = 2 : Calculate F from P,Q,DFN,DFD and PNONC C iwhich = 3 : Calculate DFN from P,Q,F,DFD and PNONC C iwhich = 4 : Calculate DFD from P,Q,F,DFN and PNONC C iwhich = 5 : Calculate PNONC from P,Q,F,DFN and DFD C INTEGER WHICH C C P <--> The integral from 0 to F of the non-central f-density. C Input range: [0,1-1E-16). C DOUBLE PRECISION P C C Q <--> 1-P. C Q is not used by this subroutine and is only included C for similarity with other cdf* routines. C DOUBLE PRECISION Q C C F <--> Upper limit of integration of the non-central 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 Must be in range: (0, +infinity). C Input range: (0, +infinity). C Search range: [ 1E-100, 1E100] C DOUBLE PRECISION DFD C C PNONC <-> The non-centrality parameter C Input range: [0,infinity) C Search range: [0,1E4] C DOUBLE PRECISION PHONC 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 26.6.20 of Abramowitz and Stegun, Handbook of C Mathematical Functions (1966) is used to compute the cumulative C distribution function. 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 computation time required for this routine is proportional C to the noncentrality parameter (PNONC). Very large values of C this parameter can consume immense computer resources. This is C why the search range is bounded by 10,000. C C WARNING C C The value of the cumulative noncentral F distribution is not C necessarily monotone in either degrees of freedom. There thus C may be two values that provide a given CDF value. This routine C assumes monotonicity and will find an arbitrary one of the two C values. C C********************************************************************** C .. Parameters .. DOUBLE PRECISION tent4 PARAMETER (tent4=1.0D4) DOUBLE PRECISION tol PARAMETER (tol=1.0D-8) DOUBLE PRECISION atol PARAMETER (atol=1.0D-50) DOUBLE PRECISION zero,one,inf PARAMETER (zero=1.0D-100,one=1.0D0-1.0D-16,inf=1.0D100) C .. C .. Scalar Arguments .. DOUBLE PRECISION bound,dfd,dfn,f,p,phonc,q INTEGER status,which C .. C .. Local Scalars .. DOUBLE PRECISION ccum,cum,fx INTEGER errflag LOGICAL qhi,qleft C .. C .. External Subroutines .. EXTERNAL cumfnc,dinvr,dstinv C .. IF (.NOT. ((which.LT.1).OR. (which.GT.5))) GO TO 30 IF (.NOT. (which.LT.1)) GO TO 10 bound = 1.0D0 GO TO 20 10 bound = 5.0D0 20 status = -1 RETURN 30 IF (which.EQ.1) GO TO 70 IF (.NOT. ((p.LT.0.0D0).OR. (p.GT.one))) GO TO 60 IF (.NOT. (p.LT.0.0D0)) GO TO 40 bound = 0.0D0 GO TO 50 40 bound = one 50 status = -2 RETURN 60 CONTINUE 70 IF (which.EQ.2) GO TO 90 IF (.NOT. (f.LT.0.0D0)) GO TO 80 bound = 0.0D0 status = -4 RETURN 80 CONTINUE 90 IF (which.EQ.3) GO TO 110 IF (.NOT. (dfn.LE.0.0D0)) GO TO 100 bound = 0.0D0 status = -5 RETURN 100 CONTINUE 110 IF (which.EQ.4) GO TO 130 IF (.NOT. (dfd.LE.0.0D0)) GO TO 120 bound = 0.0D0 status = -6 RETURN 120 CONTINUE 130 IF (which.EQ.5) GO TO 150 IF (.NOT. (phonc.LT.0.0D0)) GO TO 140 bound = 0.0D0 status = -7 RETURN 140 CONTINUE 150 IF ((1).EQ. (which)) THEN CALL cumfnc(f,dfn,dfd,phonc,p,q,errflag) IF (errflag.NE.0) THEN status = 10 RETURN ENDIF 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) 160 IF (.NOT. (status.EQ.1)) GO TO 170 CALL cumfnc(f,dfn,dfd,phonc,cum,ccum,errflag) IF (errflag.NE.0) THEN status = 10 RETURN ENDIF fx = cum - p CALL dinvr(status,f,fx,qleft,qhi) GO TO 160 170 IF (.NOT. (status.EQ.-1)) GO TO 200 IF (.NOT. (qleft)) GO TO 180 status = 1 bound = 0.0D0 GO TO 190 180 status = 2 bound = inf 190 CONTINUE 200 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) 210 IF (.NOT. (status.EQ.1)) GO TO 220 CALL cumfnc(f,dfn,dfd,phonc,cum,ccum,errflag) IF (errflag.NE.0) THEN status = 10 RETURN ENDIF fx = cum - p CALL dinvr(status,dfn,fx,qleft,qhi) GO TO 210 220 IF (.NOT. (status.EQ.-1)) GO TO 250 IF (.NOT. (qleft)) GO TO 230 status = 1 bound = zero GO TO 240 230 status = 2 bound = inf 240 CONTINUE 250 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) 260 IF (.NOT. (status.EQ.1)) GO TO 270 CALL cumfnc(f,dfn,dfd,phonc,cum,ccum,errflag) IF (errflag.NE.0) THEN status = 10 RETURN ENDIF fx = cum - p CALL dinvr(status,dfd,fx,qleft,qhi) GO TO 260 270 IF (.NOT. (status.EQ.-1)) GO TO 300 IF (.NOT. (qleft)) GO TO 280 status = 1 bound = zero GO TO 290 280 status = 2 bound = inf 290 CONTINUE 300 CONTINUE ELSE IF ((5).EQ. (which)) THEN phonc = 5.0D0 CALL dstinv(0.0D0,tent4,0.5D0,0.5D0,5.0D0,atol,tol) status = 0 CALL dinvr(status,phonc,fx,qleft,qhi) 310 IF (.NOT. (status.EQ.1)) GO TO 320 CALL cumfnc(f,dfn,dfd,phonc,cum,ccum,errflag) IF (errflag.NE.0) THEN status = 10 RETURN ENDIF fx = cum - p CALL dinvr(status,phonc,fx,qleft,qhi) GO TO 310 320 IF (.NOT. (status.EQ.-1)) GO TO 350 IF (.NOT. (qleft)) GO TO 330 status = 1 bound = 0.0D0 GO TO 340 330 status = 2 bound = tent4 340 CONTINUE 350 END IF RETURN END