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SUBROUTINE cdftnc(which,p,q,t,df,pnonc,status,bound)
C***********************************************************************
C
C SUBROUTINE CDFTNC( WHICH, P, Q, T, DF, PNONC, STATUS, BOUND )
C Cumulative Distribution Function
C Non-Central T distribution
C
C Function
C
C Calculates any one parameter of the noncentral t distribution give
C values for the others.
C
C Arguments
C
C WHICH --> Integer indicating which argument
C values is to be calculated from the others.
C Legal range: 1..3
C iwhich = 1 : Calculate P and Q from T,DF,PNONC
C iwhich = 2 : Calculate T from P,Q,DF,PNONC
C iwhich = 3 : Calculate DF from P,Q,T
C iwhich = 4 : Calculate PNONC from P,Q,DF,T
C INTEGER WHICH
C
C P <--> The integral from -infinity to t of the noncentral t-den
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 T <--> Upper limit of integration of the noncentral t-density.
C Input range: ( -infinity, +infinity).
C Search range: [ -1E100, 1E100 ]
C DOUBLE PRECISION T
C
C DF <--> Degrees of freedom of the noncentral t-distribution.
C Input range: (0 , +infinity).
C Search range: [1e-100, 1E10]
C DOUBLE PRECISION DF
C
C PNONC <--> Noncentrality parameter of the noncentral t-distributio
C Input range: [-1e6, 1E6].
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 Method
C
C Upper tail of the cumulative noncentral t is calculated usin
C formulae from page 532 of Johnson, Kotz, Balakrishnan, Coninuou
C Univariate Distributions, Vol 2, 2nd Edition. Wiley (1995)
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***********************************************************************
C .. Parameters ..
DOUBLE PRECISION tent6
PARAMETER (tent6=1.0D6)
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,df,p,pnonc,q,t
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx
LOGICAL qhi,qleft
C ..
C .. External Subroutines ..
EXTERNAL cumtnc,dinvr,dstinv
C ..
IF (t.GT.inf) THEN
t = inf
ELSE IF (t.LT.-inf) THEN
t = -inf
ENDIF
IF (df.GT.1.0D10) THEN
df = 1.0D10
ENDIF
IF (t.ne.t) THEN
status = -4
RETURN
ENDIF
IF (which.NE.4) THEN
IF (.NOT. (pnonc.GE.-tent6)) THEN
status = -6
bound = -tent6
RETURN
ELSE IF (.NOT. (pnonc.LE.tent6)) THEN
status = -6
bound = tent6
RETURN
ENDIF
ENDIF
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 = 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.3) GO TO 90
IF (df.GT.0.0D0) GO TO 80
bound = 0.0D0
status = -5
RETURN
80 CONTINUE
90 IF (which.EQ.4) GO TO 100
100 IF ((1).EQ. (which)) THEN
CALL cumtnc(t,df,pnonc,p,q)
status = 0
ELSE IF ((2).EQ. (which)) THEN
t = 5.0D0
CALL dstinv(-inf,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,t,fx,qleft,qhi)
110 IF (.NOT. (status.EQ.1)) GO TO 120
CALL cumtnc(t,df,pnonc,cum,ccum)
fx = cum - p
CALL dinvr(status,t,fx,qleft,qhi)
GO TO 110
120 IF (.NOT. (status.EQ.-1)) GO TO 150
IF (.NOT. (qleft)) GO TO 130
status = 1
bound = -inf
GO TO 140
130 status = 2
bound = inf
140 CONTINUE
150 CONTINUE
ELSE IF ((3).EQ. (which)) THEN
df = 5.0D0
CALL dstinv(zero,tent6,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,df,fx,qleft,qhi)
160 IF (.NOT. (status.EQ.1)) GO TO 170
CALL cumtnc(t,df,pnonc,cum,ccum)
fx = cum - p
CALL dinvr(status,df,fx,qleft,qhi)
GO TO 160
170 IF (.NOT. (status.EQ.-1)) GO TO 200
IF (.NOT. (qleft)) GO TO 180
status = 1
bound = zero
GO TO 190
180 status = 2
bound = inf
190 CONTINUE
200 CONTINUE
ELSE IF ((4).EQ. (which)) THEN
pnonc = 5.0D0
CALL dstinv(-tent6,tent6,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,pnonc,fx,qleft,qhi)
210 IF (.NOT. (status.EQ.1)) GO TO 220
CALL cumtnc(t,df,pnonc,cum,ccum)
fx = cum - p
CALL dinvr(status,pnonc,fx,qleft,qhi)
GO TO 210
220 IF (.NOT. (status.EQ.-1)) GO TO 250
IF (.NOT. (qleft)) GO TO 230
status = 1
bound = 0.0D0
GO TO 240
230 status = 2
bound = tent6
240 CONTINUE
250 END IF
RETURN
END
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