V138 Multinomial Random Numbers

Subroutine subprogram RNMNML generates a vector of random integers $n$_i>0  (i=1,2,...,N) with probabilities $p$_i

according to the multinomial distribution

$Prob(n$₁,n₂,...,n_N) = {(n₁+n₂+...+n_N)!n₁! n₂! ... n_N!} p₁^n₁ p₂^n₂ ... p_N^n_N .

Structure:

SUBROUTINE subprogram
User Entry Names: RNMNML
External References: RANLUX (V115)

Usage:

    CALL RNMNML(N,NSUM,PCUM,NVEC,IERR)

N

( INTEGER) Number N of random integers $n$_i

requested.

NSUM

( INTEGER) $\sum$_i=1^Nn_i , specified by the user.

PCUM

( REAL) One-dimensional array of length $\ge N$ . Must contains, on entry, the (normalized) cumulative channel probabilities $\sum$_j=1ⁱp_j

in $PCUM(i)\hspace{0.17em}(i=1,...,N)$ . In particular, $PCUM(N)=1$ .

NVEC

( INTEGER) One-dimensional array of length $\ge N$ . On exit, NVEC(i),(i = 1,...,N) contains the generated random integers.

IERR

Error flag.
$=\; 0:$ Normal case,
$=\; 1:$

for one i al least,
$=\; 2:$ $PCUM(N)\; \ne 1$ .

Notes:

For N=2, use RNBNML (V137).
$•$

V150