V137 Binomial Random Numbers

Subroutine subprogram RNBNML generates a random integer N>0 according to the binomial distribution

$Prob(N=n)\; =\; M\; nPn(1-P)M-n$

where the 'sample size' M>0 and the probability P ($0\; \le P\; \le 1$ ) are specified by the user.

Structure:

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

Usage:

    CALL RNBNML(M,P,N,IERR)

M

( INTEGER) Sample size M.

P

( REAL) Probability P.

N

( INTEGER) The generated random number N, binomially distributed in the interval $0\; \le N\; \le M$ with mean $P\; xM$ .

IERR

( INTEGER) Error flag.
$=\; 0:$ Normal case,
$=\; 1:$ $P\; \le 0$ or $P\; \ge 1$ .

Notes:

RNBNML should not be used when M is 'large' (say >100 ). The normal approximation is then recommended instead (with mean $P*M+0.5$ and standard deviation $M*P*(1-P)$ ).
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V138