rndKMnb#

Purpose#

Computes negative binomial pseudo-random numbers.

Format#

{ x, newstate } = rndKMnb(r, c, k, p, state)#
Parameters:

  • r (scalar) – number of rows of resulting matrix.

  • c (scalar) – number of columns of resulting matrix.

  • k (matrix or vector or scalar) – “event” argument for negative binomial distribution, scalar or ExE conformable matrix with r and c.

  • p (matrix or vector or scalar) – “probability” argument for negative binomial distribution, scalar or ExE conformable matrix with r and c.

  • state (scalar or 500x1 vector) –

    scalar case

    state = starting seed value only. If -1, GAUSS computes the starting seed based on the system clock.

    500x1 vector case

    state = the state vector returned from a previous call to one of the rndKM random number functions.

Returns:

  • x (RxC matrix) – negative binomial distributed random numbers.

  • newstate (500x1 vector) – the updated state.

Remarks#

The properties of the pseudo-random numbers in x are:

\[ \begin{align}\begin{aligned}E(x) = \frac{k * p}{1 - p}\\\begin{split}Var(x) = \frac{k * p}{(1 - p)^2}\\ x = 0, 1,....k > 0\\ 0 < p < 1\\\end{split}\end{aligned}\end{align} \]

r and c will be truncated to integers if necessary.

Examples#

// Generate a 3x2 matrix of negative binomial
// random numbers with k = 5 and p = 0.3
// using a fixed seed for repeatable output
{ x, newstate } = rndKMnb(3, 2, 5, 0.3, 12345);
print x;

The output is a 3x2 matrix of non-negative integers. The theoretical mean is k*p/(1-p) = 5*0.3/0.7, which is approximately 2.14:

3.0000000        1.0000000
1.0000000        3.0000000
1.0000000        1.0000000

Technical Notes#

rndKMnb() uses the recur-with-carry KISS+Monster algorithm described in the rndKMi() Technical Notes.

Source#

randkm.src

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