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SUBROUTINE cdfgam(which,p,q,x,shape,scale,status,bound)
C**********************************************************************
C
C SUBROUTINE CDFGAM( WHICH, P, Q, X, SHAPE, SCALE, STATUS, BOUND )
C Cumulative Distribution Function
C GAMma Distribution
C
C
C Function
C
C
C Calculates any one parameter of the gamma
C distribution given values for the others.
C
C
C Arguments
C
C
C WHICH --> Integer indicating which of the next four argument
C values is to be calculated from the others.
C Legal range: 1..4
C iwhich = 1 : Calculate P and Q from X,SHAPE and SCALE
C iwhich = 2 : Calculate X from P,Q,SHAPE and SCALE
C iwhich = 3 : Calculate SHAPE from P,Q,X and SCALE
C iwhich = 4 : Calculate SCALE from P,Q,X and SHAPE
C INTEGER WHICH
C
C P <--> The integral from 0 to X of the gamma 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
C X <--> The upper limit of integration of the gamma density.
C Input range: [0, +infinity).
C Search range: [0,1E100]
C DOUBLE PRECISION X
C
C SHAPE <--> The shape parameter of the gamma density.
C Input range: (0, +infinity).
C Search range: [1E-100,1E100]
C DOUBLE PRECISION SHAPE
C
C
C SCALE <--> The scale parameter of the gamma density.
C Input range: (0, +infinity).
C Search range: (1E-100,1E100]
C DOUBLE PRECISION SCALE
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 if the gamma or inverse gamma routine cannot
C compute the answer. Usually happens only for
C X and SHAPE very large (gt 1E10 or more)
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 Cumulative distribution function (P) is calculated directly by
C the code associated with:
C
C DiDinato, A. R. and Morris, A. H. Computation of the incomplete
C gamma function ratios and their inverse. ACM Trans. Math.
C Softw. 12 (1986), 377-393.
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 Note
C
C
C
C The gamma density is proportional to
C T**(SHAPE - 1) * EXP(- SCALE * T)
C
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,p,q,scale,shape,x
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx,porq,pq,xscale,xx
INTEGER ierr
LOGICAL qhi,qleft,qporq
C ..
C .. External Functions ..
DOUBLE PRECISION spmpar
EXTERNAL spmpar
C ..
C .. External Subroutines ..
EXTERNAL cumgam,dinvr,dstinv,gaminv
C ..
C .. Intrinsic Functions ..
INTRINSIC abs
C ..
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 = 4.0D0
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. (shape.LE.0.0D0)) GO TO 140
bound = 0.0D0
status = -5
RETURN
140 CONTINUE
150 IF (which.EQ.4) GO TO 170
IF (.NOT. (scale.LE.0.0D0)) GO TO 160
bound = 0.0D0
status = -6
RETURN
160 CONTINUE
170 IF (which.EQ.1) GO TO 210
pq = p + q
IF (.NOT. (abs(((pq)-0.5D0)-0.5D0).GT.
+ (3.0D0*spmpar(1)))) GO TO 200
IF (.NOT. (pq.LT.0.0D0)) GO TO 180
bound = 0.0D0
GO TO 190
180 bound = 1.0D0
190 status = 3
RETURN
200 CONTINUE
210 IF (which.EQ.1) GO TO 240
qporq = p .LE. q
IF (.NOT. (qporq)) GO TO 220
porq = p
GO TO 230
220 porq = q
230 CONTINUE
240 IF ((1).EQ. (which)) THEN
status = 0
xscale = x*scale
CALL cumgam(xscale,shape,p,q)
IF (p.GT.1.5D0) status = 10
ELSE IF ((2).EQ. (which)) THEN
CALL gaminv(shape,xx,-1.0D0,p,q,ierr)
IF (ierr.LT.0.0D0) THEN
status = 10
RETURN
ELSE
x = xx/scale
status = 0
END IF
ELSE IF ((3).EQ. (which)) THEN
shape = 5.0D0
xscale = x*scale
CALL dstinv(zero,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,shape,fx,qleft,qhi)
250 IF (.NOT. (status.EQ.1)) GO TO 290
CALL cumgam(xscale,shape,cum,ccum)
IF (.NOT. (qporq)) GO TO 260
fx = cum - p
GO TO 270
260 fx = ccum - q
270 IF (.NOT. ((qporq.AND. (cum.GT.1.5D0)).OR.
+ ((.NOT.qporq).AND. (ccum.GT.1.5D0)))) GO TO 280
status = 10
RETURN
280 CALL dinvr(status,shape,fx,qleft,qhi)
GO TO 250
290 IF (.NOT. (status.EQ.-1)) GO TO 320
IF (.NOT. (qleft)) GO TO 300
status = 1
bound = zero
GO TO 310
300 status = 2
bound = inf
310 CONTINUE
320 CONTINUE
ELSE IF ((4).EQ. (which)) THEN
CALL gaminv(shape,xx,-1.0D0,p,q,ierr)
IF (ierr.LT.0.0D0) THEN
status = 10
RETURN
ELSE
scale = xx/x
status = 0
END IF
END IF
RETURN
END
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