# rndPoisson¶

## Purpose¶

Computes Poisson pseudo-random numbers with a choice of underlying random number generator.

## Format¶

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

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

• lambda (matrix, vector or scalar) – mean parameter for Poisson distribution, ExE conformable matrix with r and c.

• state (scalar or opaque vector) –

Optional argument.

scalar case

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

opaque vector case

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

Returns:
• x (r x c matrix) – Poisson distributed random numbers.

• newstate (Opaque vector) – the updated state.

## Examples¶

The example below simulates 100 observations of a Poisson process with a mean of 17.

lambda = 17;

x = rndPoisson(100, 1, lambda);


## Remarks¶

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

\begin{align}\begin{aligned}\begin{split}E(x) = \lambda\\\end{split}\\Var(x) = \lambda\end{aligned}\end{align}

r and c will be truncated to integers if necessary.

## Technical Notes¶

The default generator for rndPoisson() is the SFMT Mersenne-Twister 19937. You can specify a different underlying random number generator with the function rndCreateState().