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SUBROUTINE genmul(n,p,ncat,ix)
C**********************************************************************
C
C SUBROUTINE GENMUL( N, P, NCAT, IX )
C GENerate an observation from the MULtinomial distribution
C
C
C Arguments
C
C
C N --> Number of events that will be classified into one of
C the categories 1..NCAT
C INTEGER N
C
C P --> Vector of probabilities. P(i) is the probability that
C an event will be classified into category i. Thus, P(i)
C must be [0,1]. Only the first NCAT-1 P(i) must be defined
C since P(NCAT) is 1.0 minus the sum of the first
C NCAT-1 P(i).
C DOUBLE PRECISION P(NCAT-1)
C
C NCAT --> Number of categories. Length of P and IX.
C INTEGER NCAT
C
C IX <-- Observation from multinomial distribution. All IX(i)
C will be nonnegative and their sum will be N.
C INTEGER IX(NCAT)
C
C
C Method
C
C
C Algorithm from page 559 of
C
C Devroye, Luc
C
C Non-Uniform Random Variate Generation. Springer-Verlag,
C New York, 1986.
C
C**********************************************************************
C .. Scalar Arguments ..
INTEGER n,ncat
C ..
C .. Array Arguments ..
DOUBLE PRECISION p(*)
INTEGER ix(*)
C ..
C .. Local Scalars ..
DOUBLE PRECISION prob,ptot,sum
INTEGER i,icat,ntot
C ..
C .. External Functions ..
INTEGER ignbin
EXTERNAL ignbin
C ..
C .. Intrinsic Functions ..
INTRINSIC abs
C ..
C .. Executable Statements ..
C Check Arguments
C see Rand.c
C Initialize variables
ntot = n
sum = 1.0
DO 20,i = 1,ncat
ix(i) = 0
20 CONTINUE
C Generate the observation
DO 30,icat = 1,ncat - 1
prob = p(icat)/sum
ix(icat) = ignbin(ntot,prob)
ntot = ntot - ix(icat)
IF (ntot.LE.0) RETURN
sum = sum - p(icat)
30 CONTINUE
ix(ncat) = ntot
C Finished
RETURN
END
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