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.

Technical Notes

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

Source

randkm.src