# rndKMp¶

## Purpose¶

Computes Poisson pseudo-random numbers.

## Format¶

{ x, newstate } = rndKMp(r, c, lambda, state)
Parameters
• r (scalar) – number of rows of resulting matrix.

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

• lambda (matrix or vector or scalar) – Shape argument for Poisson 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) – Poisson distributed random numbers.

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

## Remarks¶

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

$\begin{split}E(x) = \lambda\\ Var(x) = \lambda\\ x = 0, 1,....\\ \lambda > 0\end{split}$

r and c will be truncated to integers if necessary.

## Technical Notes¶

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

randkm.src