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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 seach 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
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)
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)
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)
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)
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)
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
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