random_multinomial

Generates pseudorandom numbers from a multinomial distribution.

Synopsis

#include <imsls.h>

int *imsls_random_multinomial(int n_random, int n, int k, float p[], …, 0)

Required Arguments

int n_random (Input)
Number of random multinomial vectors to generate.

int n (Input)
Multinomial parameter indicating the number of independent trials.

int k (Input)
The number of mutually exclusive outcomes on any trial. k is the length of the multinomial vectors. k must be greater than or equal to 2.

float p[] (Input)
Vector of length k containing the probabilities of the possible outcomes. The elements of p must be positive and must sum to 1.0.

Return Value

n_random by k matrix containing the random multinomial vectors in its rows. To release this space, use imsls_free.

Synopsis with Optional Arguments

#include <imsls.h>

int *imsls_random_multinomial (int n_random, int n, int k, float p[],
IMSLS_RETURN_USER, float r[],
0)

Optional Arguments

IMSLS_RETURN_USER, float r[] (Output)
User-supplied array of length n_random × k containing the random deviates.

Description

Function imsls_random_multinomial 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-1]) is

 

for xi ≥ 0 and

 

The deviate in each row of r is produced by generation of the binomial deviate x0 with parameters n and pi and then by successive generations of the conditional binomial deviates xj given x0, x1, …, xj−2 with parameters n - x0 - x1 - … - xj−2 and pj /(1 - p0 - p1  − … −pj−2).

Example

In this example, imsls_random_multinomial is used to generate five pseudorandom 3-dimensional multinomial variates with parameters n = 20 and p = [0.1, 0.3, 0.6].

 

#include <imsls.h>

 

int main()

{

int nr = 5, n = 20, k = 3, *ir;

float p[3] = {.1, .3, .6};

 

imsls_random_seed_set(123457);

 

ir = imsls_random_multinomial(nr, n, k, p,

0);

 

imsls_i_write_matrix("Multinomial random_deviates", 5, 3, ir,

IMSLS_NO_ROW_LABELS,

IMSLS_NO_COL_LABELS,

0);

}

Output

 

Multinomial random_deviates

5 4 11

3 6 11

3 3 14

5 5 10

4 5 11