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SUBROUTINE cdfchi(which,p,q,x,df,status,bound)
C**********************************************************************
C
C SUBROUTINE CDFCHI( WHICH, P, Q, X, DF, STATUS, BOUND )
C Cumulative Distribution Function
C CHI-Square distribution
C
C
C Function
C
C
C Calculates any one parameter of the chi-square
C distribution given values for the others.
C
C
C Arguments
C
C
C WHICH --> Integer indicating which of the next three argument
C values is to be calculated from the others.
C Legal range: 1..3
C iwhich = 1 : Calculate P and Q from X and DF
C iwhich = 2 : Calculate X from P,Q and DF
C iwhich = 3 : Calculate DF from P,Q and X
C INTEGER WHICH
C
C P <--> The integral from 0 to X of the chi-square
C distribution.
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 X <--> Upper limit of integration of the non-central
C chi-square distribution.
C Input range: [0, +infinity).
C Search range: [0,1E100]
C DOUBLE PRECISION X
C
C DF <--> Degrees of freedom of the
C chi-square distribution.
C Input range: (0, +infinity).
C Search range: [ 1E-100, 1E100]
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 10 indicates error returned from cumgam. See
C references in cdfgam
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 26.4.19 of Abramowitz and Stegun, Handbook of
C Mathematical Functions (1966) is used to reduce the chisqure
C distribution to the incomplete distribution.
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)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION bound,df,p,q,x
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx,porq,pq
LOGICAL qhi,qleft,qporq
C ..
C .. External Functions ..
DOUBLE PRECISION spmpar
EXTERNAL spmpar
C ..
C .. External Subroutines ..
EXTERNAL cumchi,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.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. (x.LT.0.0D0)) GO TO 120
bound = 0.0D0
status = -4
RETURN
120 CONTINUE
130 IF (which.EQ.3) GO TO 150
IF (.NOT. (df.LE.0.0D0)) GO TO 140
bound = 0.0D0
status = -5
RETURN
140 CONTINUE
150 IF (which.EQ.1) GO TO 190
pq = p + q
IF (.NOT. (abs(((pq)-0.5D0)-0.5D0).GT.
+ (3.0D0*spmpar(1)))) GO TO 180
IF (.NOT. (pq.LT.0.0D0)) GO TO 160
bound = 0.0D0
GO TO 170
160 bound = 1.0D0
170 status = 3
RETURN
180 CONTINUE
190 IF (which.EQ.1) GO TO 220
qporq = p .LE. q
IF (.NOT. (qporq)) GO TO 200
porq = p
GO TO 210
200 porq = q
210 CONTINUE
220 IF ((1).EQ. (which)) THEN
status = 0
CALL cumchi(x,df,p,q)
IF (porq.GT.1.5D0) THEN
status = 10
RETURN
END IF
ELSE IF ((2).EQ. (which)) THEN
x = 5.0D0
CALL dstinv(0.0D0,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,x,fx,qleft,qhi)
230 IF (.NOT. (status.EQ.1)) GO TO 270
CALL cumchi(x,df,cum,ccum)
IF (.NOT. (qporq)) GO TO 240
fx = cum - p
GO TO 250
240 fx = ccum - q
250 IF (.NOT. ((fx+porq).GT.1.5D0)) GO TO 260
status = 10
RETURN
260 CALL dinvr(status,x,fx,qleft,qhi)
GO TO 230
270 IF (.NOT. (status.EQ.-1)) GO TO 300
IF (.NOT. (qleft)) GO TO 280
status = 1
bound = 0.0D0
GO TO 290
280 status = 2
bound = inf
290 CONTINUE
300 CONTINUE
ELSE IF ((3).EQ. (which)) THEN
df = 5.0D0
CALL dstinv(zero,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,df,fx,qleft,qhi)
310 IF (.NOT. (status.EQ.1)) GO TO 350
CALL cumchi(x,df,cum,ccum)
IF (.NOT. (qporq)) GO TO 320
fx = cum - p
GO TO 330
320 fx = ccum - q
330 IF (.NOT. ((fx+porq).GT.1.5D0)) GO TO 340
status = 10
RETURN
340 CALL dinvr(status,df,fx,qleft,qhi)
GO TO 310
350 IF (.NOT. (status.EQ.-1)) GO TO 380
IF (.NOT. (qleft)) GO TO 360
status = 1
bound = zero
GO TO 370
360 status = 2
bound = inf
370 CONTINUE
380 END IF
RETURN
END
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