RNMTN
Generates pseudorandom numbers from a multinomial distribution.
Required Arguments
N — Multinomial parameter indicating the number of independent trials. (Input)
P — Vector of length K containing the probabilities of the possible outcomes. (Input)
The elements of P must be positive and must sum to 1.0.
IR — NR by K matrix containing the random multinomial vectors in its rows. (Output)
Optional Arguments
NR — Number of random multinomial vectors to generate. (Input)
Default: NR = size (IR,1).
K — The number of mutually exclusive outcomes on any trial. (Input)
K is the length of the multinomial vectors. K must be greater than or equal to 2.
Default: K = size (IR,2).
LDIR — Leading dimension of IR exactly as specified in the dimension statement of the calling program. (Input)
Default: LDIR = size (IR,1).
FORTRAN 90 Interface
Generic: CALL RNMTN (N, P, IR [, …])
Specific: The specific interface name is S_RNMTN.
FORTRAN 77 Interface
Single: CALL RNMTN (NR, N, K, P, IR, LDIR)
Description
Routine RNMTN generates pseudorandom numbers from a K‑variate multinomial distribution with parameters N and P. K and N must be positive. Each element of P must be positive and the elements must sum to 1. The probability function (with n = N, k = K, and pi = P(I)) is
for xi ≥ 0 and
The deviate in each row of IR is produced by generation of the binomial deviate x1with parameters n and pi and then by successive generations of the conditional binomial deviates xj given x1, x2, …, xj−1 with parameters n – x1 ‑ x2 ‑ … – xj−1 and pj /(1 ‑ p1 ‑ p2 ‑ … ‑ pj−1).
Comments
The routine
RNSET can be used to initialize the seed of the random number generator. The routine
RNOPT can be used to select the form of the generator.
Example
In this example, RNMTN is used to generate five pseudorandom 3‑dimensional multinomial variates with parameters N = 20 and P = (0.1, 0.3, 0.6).
USE RNMTN_INT
USE UMACH_INT
USE RNSET_INT
IMPLICIT NONE
INTEGER K, LDIR
PARAMETER (K=3, LDIR=5)
!
INTEGER I, IR(LDIR,K), ISEED, J, N, NOUT, NR
REAL P(K)
!
CALL UMACH (2, NOUT)
N = 20
NR = 5
P(1) = 0.1
P(2) = 0.3
P(3) = 0.6
ISEED = 123457
CALL RNSET (ISEED)
CALL RNMTN (N, P, IR)
WRITE (NOUT,99999) ((IR(I,J),J=1,K),I=1,NR)
99999 FORMAT (' Multinomial random deviates: ', 3I4, /, (30X,3I4))
END
Output
Multinomial random deviates: 5 4 11
3 6 11
3 3 14
5 5 10
4 5 11
