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SUBROUTINE cdfbet(which,p,q,x,y,a,b,status,bound)
C**********************************************************************
C
C SUBROUTINE CDFBET( WHICH, P, Q, X, Y, A, B, STATUS, BOUND )
C Cumulative Distribution Function
C BETa Distribution
C
C
C Function
C
C
C Calculates any one parameter of the beta distribution given
C 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,Y,A and B
C iwhich = 2 : Calculate X and Y from P,Q,A and B
C iwhich = 3 : Calculate A from P,Q,X,Y and B
C iwhich = 4 : Calculate B from P,Q,X,Y and A
C
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 beta density.
C Input range: [0,1].
C Search range: [0,1]
C DOUBLE PRECISION X
C
C Y <--> 1-X.
C Input range: [0,1].
C Search range: [0,1]
C X + Y = 1.0.
C DOUBLE PRECISION Y
C
C A <--> The first parameter of the beta density.
C Input range: (0, +infinity).
C Search range: [1D-100,1D100]
C DOUBLE PRECISION A
C
C B <--> The second parameter of the beta density.
C Input range: (0, +infinity).
C Search range: [1D-100,1D100]
C DOUBLE PRECISION B
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 4 if X + Y .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 Cumulative distribution function (P) is calculated directly by
C code associated with the following reference.
C
C DiDinato, A. R. and Morris, A. H. Algorithm 708: Significant
C Digit Computation of the Incomplete Beta Function Ratios. ACM
C Trans. Math. Softw. 18 (1993), 360-373.
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 The beta density is proportional to
C t^(A-1) * (1-t)^(B-1)
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 one
PARAMETER (one=1.0D0)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION a,b,bound,p,q,x,y
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx,pq,xhi,xlo,xy
LOGICAL qhi,qleft,qporq
C ..
C .. External Functions ..
DOUBLE PRECISION spmpar
EXTERNAL spmpar
C ..
C .. External Subroutines ..
EXTERNAL cumbet,dinvr,dstinv,dstzr,dzror
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.LT.0.0D0).OR. (q.GT.1.0D0))) GO TO 100
IF (.NOT. (q.LT.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 150
IF (.NOT. ((x.LT.0.0D0).OR. (x.GT.1.0D0))) GO TO 140
IF (.NOT. (x.LT.0.0D0)) GO TO 120
bound = 0.0D0
GO TO 130
120 bound = 1.0D0
130 status = -4
RETURN
140 CONTINUE
150 IF (which.EQ.2) GO TO 190
IF (.NOT. ((y.LT.0.0D0).OR. (y.GT.1.0D0))) GO TO 180
IF (.NOT. (y.LT.0.0D0)) GO TO 160
bound = 0.0D0
GO TO 170
160 bound = 1.0D0
170 status = -5
RETURN
180 CONTINUE
190 IF (which.EQ.3) GO TO 210
IF (.NOT. (a.LE.0.0D0)) GO TO 200
bound = 0.0D0
status = -6
RETURN
200 CONTINUE
210 IF (which.EQ.4) GO TO 230
IF (.NOT. (b.LE.0.0D0)) GO TO 220
bound = 0.0D0
status = -7
RETURN
220 CONTINUE
230 IF (which.EQ.1) GO TO 270
pq = p + q
IF (.NOT. (abs(((pq)-0.5D0)-0.5D0).GT.
+ (3.0D0*spmpar(1)))) GO TO 260
IF (.NOT. (pq.LT.0.0D0)) GO TO 240
bound = 0.0D0
GO TO 250
240 bound = 1.0D0
250 status = 3
RETURN
260 CONTINUE
270 IF (which.EQ.2) GO TO 310
xy = x + y
IF (.NOT. (abs(((xy)-0.5D0)-0.5D0).GT.
+ (3.0D0*spmpar(1)))) GO TO 300
IF (.NOT. (xy.LT.0.0D0)) GO TO 280
bound = 0.0D0
GO TO 290
280 bound = 1.0D0
290 status = 4
RETURN
300 CONTINUE
310 IF (.NOT. (which.EQ.1)) qporq = p .LE. q
IF ((1).EQ. (which)) THEN
CALL cumbet(x,y,a,b,p,q)
status = 0
ELSE IF ((2).EQ. (which)) THEN
CALL dstzr(0.0D0,1.0D0,atol,tol)
IF (.NOT. (qporq)) GO TO 340
status = 0
CALL dzror(status,x,fx,xlo,xhi,qleft,qhi)
y = one - x
320 IF (.NOT. (status.EQ.1)) GO TO 330
CALL cumbet(x,y,a,b,cum,ccum)
fx = cum - p
CALL dzror(status,x,fx,xlo,xhi,qleft,qhi)
y = one - x
GO TO 320
330 GO TO 370
340 status = 0
CALL dzror(status,y,fx,xlo,xhi,qleft,qhi)
x = one - y
350 IF (.NOT. (status.EQ.1)) GO TO 360
CALL cumbet(x,y,a,b,cum,ccum)
fx = ccum - q
CALL dzror(status,y,fx,xlo,xhi,qleft,qhi)
x = one - y
GO TO 350
360 CONTINUE
370 IF (.NOT. (status.EQ.-1)) GO TO 400
IF (.NOT. (qleft)) GO TO 380
status = 1
bound = 0.0D0
GO TO 390
380 status = 2
bound = 1.0D0
390 CONTINUE
400 CONTINUE
ELSE IF ((3).EQ. (which)) THEN
a = 5.0D0
CALL dstinv(zero,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,a,fx,qleft,qhi)
410 IF (.NOT. (status.EQ.1)) GO TO 440
CALL cumbet(x,y,a,b,cum,ccum)
IF (.NOT. (qporq)) GO TO 420
fx = cum - p
GO TO 430
420 fx = ccum - q
430 CALL dinvr(status,a,fx,qleft,qhi)
GO TO 410
440 IF (.NOT. (status.EQ.-1)) GO TO 470
IF (.NOT. (qleft)) GO TO 450
status = 1
bound = zero
GO TO 460
450 status = 2
bound = inf
460 CONTINUE
470 CONTINUE
ELSE IF ((4).EQ. (which)) THEN
b = 5.0D0
CALL dstinv(zero,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,b,fx,qleft,qhi)
480 IF (.NOT. (status.EQ.1)) GO TO 510
CALL cumbet(x,y,a,b,cum,ccum)
IF (.NOT. (qporq)) GO TO 490
fx = cum - p
GO TO 500
490 fx = ccum - q
500 CALL dinvr(status,b,fx,qleft,qhi)
GO TO 480
510 IF (.NOT. (status.EQ.-1)) GO TO 540
IF (.NOT. (qleft)) GO TO 520
status = 1
bound = zero
GO TO 530
520 status = 2
bound = inf
530 CONTINUE
540 END IF
RETURN
END
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