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SUBROUTINE cdft(which,p,q,t,df,status,bound)
C**********************************************************************
C
C SUBROUTINE CDFT( WHICH, P, Q, T, DF, STATUS, BOUND )
C Cumulative Distribution Function
C T distribution
C
C
C Function
C
C
C Calculates any one parameter of the t distribution given
C values for the others.
C
C
C Arguments
C
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 and DF
C iwhich = 2 : Calculate T from P,Q and DF
C iwhich = 3 : Calculate DF from P,Q and T
C INTEGER WHICH
C
C P <--> The integral from -infinity to t of the t-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 T <--> Upper limit of integration of the t-density.
C Input range: ( -infinity, +infinity).
C Search range: [ -1E100, 1E100 ]
C DOUBLE PRECISION T
C
C DF <--> Degrees of freedom of the t-distribution.
C Input range: (0 , +infinity).
C Search range: [1e-100, 1E10]
C DOUBLE PRECISION DF
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 26.5.27 of Abramowitz and Stegun, Handbook of
C Mathematical Functions (1966) is used to reduce the computation
C of the cumulative distribution function to that of an incomplete
C beta.
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 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)
DOUBLE PRECISION rtinf
PARAMETER (rtinf=1.0D100)
DOUBLE PRECISION maxdf
PARAMETER (maxdf=1.0d10)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION bound,df,p,q,t
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx,pq
LOGICAL qhi,qleft,qporq
C ..
C .. External Functions ..
DOUBLE PRECISION dt1,spmpar
EXTERNAL dt1,spmpar
C ..
C .. External Subroutines ..
EXTERNAL cumt,dinvr,dstinv
C ..
C .. Intrinsic Functions ..
INTRINSIC abs
C ..
IF (.NOT. ((which.LT.1).OR. (which.GT.3))) GO TO 30
IF (.NOT. (which.LT.1)) GO TO 10
bound = 1.0D0
GO TO 20
10 bound = 3.0D0
20 status = -1
RETURN
30 IF (which.EQ.1) GO TO 70
IF (.NOT. ((p.LE.0.0D0).OR. (p.GT.1.0D0))) GO TO 60
IF (.NOT. (p.LE.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.3) GO TO 130
IF (.NOT. (df.LE.0.0D0)) GO TO 120
bound = 0.0D0
status = -5
RETURN
120 CONTINUE
130 IF (which.EQ.1) GO TO 170
pq = p + q
IF (.NOT. (abs(((pq)-0.5D0)-0.5D0).GT.
+ (3.0D0*spmpar(1)))) GO TO 160
IF (.NOT. (pq.LT.0.0D0)) GO TO 140
bound = 0.0D0
GO TO 150
140 bound = 1.0D0
150 status = 3
RETURN
160 CONTINUE
170 IF (.NOT. (which.EQ.1)) qporq = p .LE. q
IF ((1).EQ. (which)) THEN
CALL cumt(t,df,p,q)
status = 0
ELSE IF ((2).EQ. (which)) THEN
t = dt1(p,q,df)
CALL dstinv(-rtinf,rtinf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,t,fx,qleft,qhi)
180 IF (.NOT. (status.EQ.1)) GO TO 210
CALL cumt(t,df,cum,ccum)
IF (.NOT. (qporq)) GO TO 190
fx = cum - p
GO TO 200
190 fx = ccum - q
200 CALL dinvr(status,t,fx,qleft,qhi)
GO TO 180
210 IF (.NOT. (status.EQ.-1)) GO TO 240
IF (.NOT. (qleft)) GO TO 220
status = 1
bound = -rtinf
GO TO 230
220 status = 2
bound = rtinf
230 CONTINUE
240 CONTINUE
ELSE IF ((3).EQ. (which)) THEN
df = 5.0D0
CALL dstinv(zero,maxdf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,df,fx,qleft,qhi)
250 IF (.NOT. (status.EQ.1)) GO TO 280
CALL cumt(t,df,cum,ccum)
IF (.NOT. (qporq)) GO TO 260
fx = cum - p
GO TO 270
260 fx = ccum - q
270 CALL dinvr(status,df,fx,qleft,qhi)
GO TO 250
280 IF (.NOT. (status.EQ.-1)) GO TO 310
IF (.NOT. (qleft)) GO TO 290
status = 1
bound = zero
GO TO 300
290 status = 2
bound = maxdf
300 CONTINUE
310 END IF
RETURN
END
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