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SUBROUTINE cdfpoi(which,p,q,s,xlam,status,bound)
C**********************************************************************
C
C SUBROUTINE CDFPOI( WHICH, P, Q, S, XLAM, STATUS, BOUND )
C Cumulative Distribution Function
C POIsson distribution
C
C
C Function
C
C
C Calculates any one parameter of the Poisson
C distribution given values for the others.
C
C
C Arguments
C
C
C WHICH --> Integer indicating which argument
C value is to be calculated from the others.
C Legal range: 1..3
C iwhich = 1 : Calculate P and Q from S and XLAM
C iwhich = 2 : Calculate S from P,Q and XLAM
C iwhich = 3 : Calculate XLAM from P,Q and S
C INTEGER WHICH
C
C P <--> The cumulation from 0 to S of the poisson 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 S <--> Upper limit of cumulation of the Poisson.
C Input range: [0, +infinity).
C Search range: [0,1E100]
C DOUBLE PRECISION S
C
C XLAM <--> Mean of the Poisson distribution.
C Input range: [0, +infinity).
C Search range: [0,1E100]
C DOUBLE PRECISION XLAM
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 26.4.21 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 computing a
C chi-square, hence an incomplete gamma function.
C
C Cumulative distribution function (P) is calculated directly.
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**********************************************************************
IMPLICIT NONE
C .. Parameters ..
DOUBLE PRECISION tol
PARAMETER (tol=1.0D-8)
DOUBLE PRECISION atol
PARAMETER (atol=1.0D-50)
DOUBLE PRECISION inf
PARAMETER (inf=1.0D100)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION bound,p,q,s,xlam
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx,pq
LOGICAL qhi,qleft,qporq
C ..
C .. External Functions ..
DOUBLE PRECISION spmpar
EXTERNAL spmpar
C ..
C .. External Subroutines ..
EXTERNAL cumpoi,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. (s.LT.0.0D0)) GO TO 120
bound = 0.0D0
status = -4
RETURN
120 CONTINUE
130 IF (which.EQ.3) GO TO 150
IF (.NOT. (xlam.LT.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 (.NOT. (which.EQ.1)) qporq = p .LE. q
IF ((1).EQ. (which)) THEN
CALL cumpoi(s,xlam,p,q)
status = 0
ELSE IF ((2).EQ. (which)) THEN
IF ((xlam .LT. 1.0D-2) .AND. (p .LT. 0.975D0)) THEN
C For sufficiently small xlam and p, the result is 0.0.
s = 0.0D0
status = 0
GO TO 260
END IF
s = 5.0D0
CALL dstinv(0.0D0,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,s,fx,qleft,qhi)
200 IF (.NOT. (status.EQ.1)) GO TO 230
CALL cumpoi(s,xlam,cum,ccum)
IF (.NOT. (qporq)) GO TO 210
fx = cum - p
GO TO 220
210 fx = ccum - q
220 CALL dinvr(status,s,fx,qleft,qhi)
GO TO 200
230 IF (.NOT. (status.EQ.-1)) GO TO 260
IF (.NOT. (qleft)) GO TO 240
status = 1
bound = 0.0D0
GO TO 250
240 status = 2
bound = inf
250 CONTINUE
260 CONTINUE
ELSE IF ((3).EQ. (which)) THEN
xlam = 5.0D0
CALL dstinv(0.0D0,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,xlam,fx,qleft,qhi)
270 IF (.NOT. (status.EQ.1)) GO TO 300
CALL cumpoi(s,xlam,cum,ccum)
IF (.NOT. (qporq)) GO TO 280
fx = cum - p
GO TO 290
280 fx = ccum - q
290 CALL dinvr(status,xlam,fx,qleft,qhi)
GO TO 270
300 IF (.NOT. (status.EQ.-1)) GO TO 330
IF (.NOT. (qleft)) GO TO 310
status = 1
bound = 0.0D0
GO TO 320
310 status = 2
bound = inf
320 CONTINUE
330 END IF
RETURN
END
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