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INTEGER FUNCTION ignbin(n,pp)
C**********************************************************************
C
C INTEGER FUNCTION IGNBIN( N, PP )
C
C GENerate BINomial random deviate
C
C
C Function
C
C
C Generates a single random deviate from a binomial
C distribution whose number of trials is N and whose
C probability of an event in each trial is P.
C
C
C Arguments
C
C
C N --> The number of trials in the binomial distribution
C from which a random deviate is to be generated.
C INTEGER N
C JJV (N >= 0)
C
C PP --> The probability of an event in each trial of the
C binomial distribution from which a random deviate
C is to be generated.
C DOUBLE PRECISION PP
C JJV (0.0 <= pp <= 1.0)
C
C IGNBIN <-- A random deviate yielding the number of events
C from N independent trials, each of which has
C a probability of event P.
C INTEGER IGNBIN
C
C
C Note
C
C
C Uses RANF so the value of the seeds, ISEED1 and ISEED2 must be set
C by a call similar to the following
C DUM = RANSET( ISEED1, ISEED2 )
C
C
C Method
C
C
C This is algorithm BTPE from:
C
C Kachitvichyanukul, V. and Schmeiser, B. W.
C
C Binomial Random Variate Generation.
C Communications of the ACM, 31, 2
C (February, 1988) 216.
C
C**********************************************************************
C SUBROUTINE BTPEC(N,PP,ISEED,JX)
C
C BINOMIAL RANDOM VARIATE GENERATOR
C MEAN .LT. 30 -- INVERSE CDF
C MEAN .GE. 30 -- ALGORITHM BTPE: ACCEPTANCE-REJECTION VIA
C FOUR REGION COMPOSITION. THE FOUR REGIONS ARE A TRIANGLE
C (SYMMETRIC IN THE CENTER), A PAIR OF PARALLELOGRAMS (ABOVE
C THE TRIANGLE), AND EXPONENTIAL LEFT AND RIGHT TAILS.
C
C BTPE REFERS TO BINOMIAL-TRIANGLE-PARALLELOGRAM-EXPONENTIAL.
C BTPEC REFERS TO BTPE AND "COMBINED." THUS BTPE IS THE
C RESEARCH AND BTPEC IS THE IMPLEMENTATION OF A COMPLETE
C USABLE ALGORITHM.
C REFERENCE: VORATAS KACHITVICHYANUKUL AND BRUCE SCHMEISER,
C "BINOMIAL RANDOM VARIATE GENERATION,"
C COMMUNICATIONS OF THE ACM, FORTHCOMING
C WRITTEN: SEPTEMBER 1980.
C LAST REVISED: MAY 1985, JULY 1987
C REQUIRED SUBPROGRAM: RAND() -- A UNIFORM (0,1) RANDOM NUMBER
C GENERATOR
C ARGUMENTS
C
C N : NUMBER OF BERNOULLI TRIALS (INPUT)
C PP : PROBABILITY OF SUCCESS IN EACH TRIAL (INPUT)
C ISEED: RANDOM NUMBER SEED (INPUT AND OUTPUT)
C JX: RANDOMLY GENERATED OBSERVATION (OUTPUT)
C
C VARIABLES
C PSAVE: VALUE OF PP FROM THE LAST CALL TO BTPEC
C NSAVE: VALUE OF N FROM THE LAST CALL TO BTPEC
C XNP: VALUE OF THE MEAN FROM THE LAST CALL TO BTPEC
C
C P: PROBABILITY USED IN THE GENERATION PHASE OF BTPEC
C FFM: TEMPORARY VARIABLE EQUAL TO XNP + P
C M: INTEGER VALUE OF THE CURRENT MODE
C FM: FLOATING POINT VALUE OF THE CURRENT MODE
C XNPQ: TEMPORARY VARIABLE USED IN SETUP AND SQUEEZING STEPS
C P1: AREA OF THE TRIANGLE
C C: HEIGHT OF THE PARALLELOGRAMS
C XM: CENTER OF THE TRIANGLE
C XL: LEFT END OF THE TRIANGLE
C XR: RIGHT END OF THE TRIANGLE
C AL: TEMPORARY VARIABLE
C XLL: RATE FOR THE LEFT EXPONENTIAL TAIL
C XLR: RATE FOR THE RIGHT EXPONENTIAL TAIL
C P2: AREA OF THE PARALLELOGRAMS
C P3: AREA OF THE LEFT EXPONENTIAL TAIL
C P4: AREA OF THE RIGHT EXPONENTIAL TAIL
C U: A U(0,P4) RANDOM VARIATE USED FIRST TO SELECT ONE OF THE
C FOUR REGIONS AND THEN CONDITIONALLY TO GENERATE A VALUE
C FROM THE REGION
C V: A U(0,1) RANDOM NUMBER USED TO GENERATE THE RANDOM VALUE
C (REGION 1) OR TRANSFORMED INTO THE VARIATE TO ACCEPT OR
C REJECT THE CANDIDATE VALUE
C IX: INTEGER CANDIDATE VALUE
C X: PRELIMINARY CONTINUOUS CANDIDATE VALUE IN REGION 2 LOGIC
C AND A FLOATING POINT IX IN THE ACCEPT/REJECT LOGIC
C K: ABSOLUTE VALUE OF (IX-M)
C F: THE HEIGHT OF THE SCALED DENSITY FUNCTION USED IN THE
C ACCEPT/REJECT DECISION WHEN BOTH M AND IX ARE SMALL
C ALSO USED IN THE INVERSE TRANSFORMATION
C R: THE RATIO P/Q
C G: CONSTANT USED IN CALCULATION OF PROBABILITY
C MP: MODE PLUS ONE, THE LOWER INDEX FOR EXPLICIT CALCULATION
C OF F WHEN IX IS GREATER THAN M
C IX1: CANDIDATE VALUE PLUS ONE, THE LOWER INDEX FOR EXPLICIT
C CALCULATION OF F WHEN IX IS LESS THAN M
C I: INDEX FOR EXPLICIT CALCULATION OF F FOR BTPE
C AMAXP: MAXIMUM ERROR OF THE LOGARITHM OF NORMAL BOUND
C YNORM: LOGARITHM OF NORMAL BOUND
C ALV: NATURAL LOGARITHM OF THE ACCEPT/REJECT VARIATE V
C
C X1,F1,Z,W,Z2,X2,F2, AND W2 ARE TEMPORARY VARIABLES TO BE
C USED IN THE FINAL ACCEPT/REJECT TEST
C
C QN: PROBABILITY OF NO SUCCESS IN N TRIALS
C
C REMARK
C IX AND JX COULD LOGICALLY BE THE SAME VARIABLE, WHICH WOULD
C SAVE A MEMORY POSITION AND A LINE OF CODE. HOWEVER, SOME
C COMPILERS (E.G.,CDC MNF) OPTIMIZE BETTER WHEN THE ARGUMENTS
C ARE NOT INVOLVED.
C
C ISEED NEEDS TO BE DOUBLE PRECISION IF THE IMSL ROUTINE
C GGUBFS IS USED TO GENERATE UNIFORM RANDOM NUMBER, OTHERWISE
C TYPE OF ISEED SHOULD BE DICTATED BY THE UNIFORM GENERATOR
C
C**********************************************************************
C
C
C
C*****DETERMINE APPROPRIATE ALGORITHM AND WHETHER SETUP IS NECESSARY
C
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION pp
INTEGER n
C ..
C .. Local Scalars ..
DOUBLE PRECISION al,alv,amaxp,c,f,f1,f2,ffm,fm,g,p,p1,p2,p3,p4,
+ psave,q,qn,r,u,
+ v,w,w2,x,x1,x2,xl,xll,xlr,xm,xnp,xnpq,xr,ynorm,z,z2
INTEGER i,ix,ix1,k,m,mp,nsave
C ..
C .. External Functions ..
DOUBLE PRECISION ranf
EXTERNAL ranf
C ..
C .. Intrinsic Functions ..
INTRINSIC abs,log,dmin1,iabs,int,sqrt
C JJV ..
C JJV .. Save statement ..
SAVE p,q,m,fm,xnp,xnpq,p1,xm,xl,xr,c,xll,xlr,p2,p3,p4,qn,r,g,
+ psave,nsave
C JJV I am including the variables in data statements
C ..
C .. Data statements ..
C JJV made these ridiculous starting values - the hope is that
C JJV no one will call this the first time with them as args
DATA psave,nsave/-1.0E37,-214748365/
C ..
C .. Executable Statements ..
IF (pp.NE.psave) GO TO 10
IF (n.NE.nsave) GO TO 20
IF (xnp-30.) 150,30,30
C
C*****SETUP, PERFORM ONLY WHEN PARAMETERS CHANGE
C
C JJV added the argument checker - involved only renaming 10
C JJV and 20 to the checkers and adding checkers
C JJV Only remaining problem - if called initially with the
C JJV initial values of psave and nsave, it will hang
10 continue
psave = pp
p = dmin1(psave,1.-psave)
q = 1. - p
20 continue
xnp = n*p
nsave = n
IF (xnp.LT.30.) GO TO 140
ffm = xnp + p
m = ffm
fm = m
xnpq = xnp*q
p1 = int(2.195*sqrt(xnpq)-4.6*q) + 0.5
xm = fm + 0.5
xl = xm - p1
xr = xm + p1
c = 0.134 + 20.5/ (15.3+fm)
al = (ffm-xl)/ (ffm-xl*p)
xll = al* (1.+.5*al)
al = (xr-ffm)/ (xr*q)
xlr = al* (1.+.5*al)
p2 = p1* (1.+c+c)
p3 = p2 + c/xll
p4 = p3 + c/xlr
C WRITE(6,100) N,P,P1,P2,P3,P4,XL,XR,XM,FM
C 100 FORMAT(I15,4F18.7/5F18.7)
C
C*****GENERATE VARIATE
C
30 u = ranf()*p4
v = ranf()
C
C TRIANGULAR REGION
C
IF (u.GT.p1) GO TO 40
ix = xm - p1*v + u
GO TO 170
C
C PARALLELOGRAM REGION
C
40 IF (u.GT.p2) GO TO 50
x = xl + (u-p1)/c
v = v*c + 1. - abs(xm-x)/p1
IF (v.GT.1. .OR. v.LE.0.) GO TO 30
ix = x
GO TO 70
C
C LEFT TAIL
C
50 IF (u.GT.p3) GO TO 60
ix = xl + log(v)/xll
IF (ix.LT.0) GO TO 30
v = v* (u-p2)*xll
GO TO 70
C
C RIGHT TAIL
C
60 ix = xr - log(v)/xlr
IF (ix.GT.n) GO TO 30
v = v* (u-p3)*xlr
C
C*****DETERMINE APPROPRIATE WAY TO PERFORM ACCEPT/REJECT TEST
C
70 k = iabs(ix-m)
IF (k.GT.20 .AND. k.LT.xnpq/2-1) GO TO 130
C
C EXPLICIT EVALUATION
C
f = 1.0
r = p/q
g = (n+1)*r
IF (m-ix) 80,120,100
80 mp = m + 1
DO 90 i = mp,ix
f = f* (g/i-r)
90 CONTINUE
GO TO 120
100 ix1 = ix + 1
DO 110 i = ix1,m
f = f/ (g/i-r)
110 CONTINUE
120 IF (v-f) 170,170,30
C
C SQUEEZING USING UPPER AND LOWER BOUNDS ON LOG(F(X))
C
130 amaxp = (k/xnpq)* ((k* (k/3.+.625)+.1666666666666)/xnpq+.5)
ynorm = -k*k/ (2.*xnpq)
alv = log(v)
IF (alv.LT.ynorm-amaxp) GO TO 170
IF (alv.GT.ynorm+amaxp) GO TO 30
C
C STIRLING'S FORMULA TO MACHINE ACCURACY FOR
C THE FINAL ACCEPTANCE/REJECTION TEST
C
x1 = ix + 1
f1 = fm + 1.
z = n + 1 - fm
w = n - ix + 1.
z2 = z*z
x2 = x1*x1
f2 = f1*f1
w2 = w*w
IF (alv- (xm*log(f1/x1)+ (n-m+.5)*log(z/w)+ (ix-
+ m)*log(w*p/ (x1*q))+ (13860.- (462.- (132.- (99.-
+ 140./f2)/f2)/f2)/f2)/f1/166320.+ (13860.- (462.- (132.- (99.-
+ 140./z2)/z2)/z2)/z2)/z/166320.+ (13860.- (462.- (132.- (99.-
+ 140./x2)/x2)/x2)/x2)/x1/166320.+ (13860.- (462.- (132.- (99.-
+ 140./w2)/w2)/w2)/w2)/w/166320.)) 170,170,30
C
C INVERSE CDF LOGIC FOR MEAN LESS THAN 30
C
140 qn = q**n
r = p/q
g = r* (n+1)
150 ix = 0
f = qn
u = ranf()
160 IF (u.LT.f) GO TO 170
IF (ix.GT.110) GO TO 150
u = u - f
ix = ix + 1
f = f* (g/ix-r)
GO TO 160
170 IF (psave.GT.0.5) ix = n - ix
ignbin = ix
RETURN
END
|
