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SUBROUTINE cdfnbn(which,p,q,s,xn,pr,ompr,status,bound)
C**********************************************************************
C
C SUBROUTINE CDFNBN ( WHICH, P, S, XN, PR, STATUS, BOUND )
C Cumulative Distribution Function
C Negative BiNomial distribution
C
C
C Function
C
C
C Calculates any one parameter of the negative binomial
C distribution given values for the others.
C
C The cumulative negative binomial distribution returns the
C probability that there will be F or fewer failures before the
C XNth success in binomial trials each of which has probability of
C success PR.
C
C The individual term of the negative binomial is the probability of
C S failures before XN successes and is
C Choose( S, XN+S-1 ) * PR^(XN) * (1-PR)^S
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 S,XN,PR and OMPR
C iwhich = 2 : Calculate S from P,Q,XN,PR and OMPR
C iwhich = 3 : Calculate XN from P,Q,S,PR and OMPR
C iwhich = 4 : Calculate PR and OMPR from P,Q,S and XN
C INTEGER WHICH
C
C P <--> The cumulation from 0 to S of the negative
C binomial 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 S <--> The upper limit of cumulation of the binomial distribution.
C There are F or fewer failures before the XNth success.
C Input range: [0, +infinity).
C Search range: [0, 1E100]
C DOUBLE PRECISION S
C
C XN <--> The number of successes.
C Input range: [0, +infinity).
C Search range: [0, 1E100]
C DOUBLE PRECISION XN
C
C PR <--> The probability of success in each binomial trial.
C Input range: [0,1].
C Search range: [0,1].
C DOUBLE PRECISION PR
C
C OMPR <--> 1-PR
C Input range: [0,1].
C Search range: [0,1]
C PR + OMPR = 1.0
C DOUBLE PRECISION OMPR
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 PR + OMPR .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 26.5.26 of Abramowitz and Stegun, Handbook of
C Mathematical Functions (1966) is used to reduce calculation of
C 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**********************************************************************
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)
DOUBLE PRECISION one
PARAMETER (one=1.0D0)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION bound,ompr,p,pr,q,s,xn
INTEGER status,which
C ..
C .. Local Scalars ..
DOUBLE PRECISION ccum,cum,fx,pq,prompr,xhi,xlo
LOGICAL qhi,qleft,qporq
C ..
C .. External Functions ..
DOUBLE PRECISION spmpar
EXTERNAL spmpar
C ..
C .. External Subroutines ..
EXTERNAL cumnbn,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.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. (xn.LT.0.0D0)) GO TO 140
bound = 0.0D0
status = -5
RETURN
140 CONTINUE
150 IF (which.EQ.4) GO TO 190
IF (.NOT. ((pr.LT.0.0D0).OR. (pr.GT.1.0D0))) GO TO 180
IF (.NOT. (pr.LT.0.0D0)) GO TO 160
bound = 0.0D0
GO TO 170
160 bound = 1.0D0
170 status = -6
RETURN
180 CONTINUE
190 IF (which.EQ.4) GO TO 230
IF (.NOT. ((ompr.LT.0.0D0).OR. (ompr.GT.1.0D0))) GO TO 220
IF (.NOT. (ompr.LT.0.0D0)) GO TO 200
bound = 0.0D0
GO TO 210
200 bound = 1.0D0
210 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.4) GO TO 310
prompr = pr + ompr
IF (.NOT. (abs(((prompr)-0.5D0)-0.5D0).GT.
+ (3.0D0*spmpar(1)))) GO TO 300
IF (.NOT. (prompr.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 cumnbn(s,xn,pr,ompr,p,q)
status = 0
ELSE IF ((2).EQ. (which)) THEN
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)
320 IF (.NOT. (status.EQ.1)) GO TO 350
CALL cumnbn(s,xn,pr,ompr,cum,ccum)
IF (.NOT. (qporq)) GO TO 330
fx = cum - p
GO TO 340
330 fx = ccum - q
340 CALL dinvr(status,s,fx,qleft,qhi)
GO TO 320
350 IF (.NOT. (status.EQ.-1)) GO TO 380
IF (.NOT. (qleft)) GO TO 360
status = 1
bound = 0.0D0
GO TO 370
360 status = 2
bound = inf
370 CONTINUE
380 CONTINUE
ELSE IF ((3).EQ. (which)) THEN
xn = 5.0D0
CALL dstinv(0.0D0,inf,0.5D0,0.5D0,5.0D0,atol,tol)
status = 0
CALL dinvr(status,xn,fx,qleft,qhi)
390 IF (.NOT. (status.EQ.1)) GO TO 420
CALL cumnbn(s,xn,pr,ompr,cum,ccum)
IF (.NOT. (qporq)) GO TO 400
fx = cum - p
GO TO 410
400 fx = ccum - q
410 CALL dinvr(status,xn,fx,qleft,qhi)
GO TO 390
420 IF (.NOT. (status.EQ.-1)) GO TO 450
IF (.NOT. (qleft)) GO TO 430
status = 1
bound = 0.0D0
GO TO 440
430 status = 2
bound = inf
440 CONTINUE
450 CONTINUE
ELSE IF ((4).EQ. (which)) THEN
CALL dstzr(0.0D0,1.0D0,atol,tol)
IF (.NOT. (qporq)) GO TO 480
status = 0
CALL dzror(status,pr,fx,xlo,xhi,qleft,qhi)
ompr = one - pr
460 IF (.NOT. (status.EQ.1)) GO TO 470
CALL cumnbn(s,xn,pr,ompr,cum,ccum)
fx = cum - p
CALL dzror(status,pr,fx,xlo,xhi,qleft,qhi)
ompr = one - pr
GO TO 460
470 GO TO 510
480 status = 0
CALL dzror(status,ompr,fx,xlo,xhi,qleft,qhi)
pr = one - ompr
490 IF (.NOT. (status.EQ.1)) GO TO 500
CALL cumnbn(s,xn,pr,ompr,cum,ccum)
fx = ccum - q
CALL dzror(status,ompr,fx,xlo,xhi,qleft,qhi)
pr = one - ompr
GO TO 490
500 CONTINUE
510 IF (.NOT. (status.EQ.-1)) GO TO 540
IF (.NOT. (qleft)) GO TO 520
status = 1
bound = 0.0D0
GO TO 530
520 status = 2
bound = 1.0D0
530 CONTINUE
540 END IF
RETURN
END
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