# rndExp#

## Purpose#

Computes exponentially distributed random numbers with a choice of underlying random number generator.

## Format#

r = rndExp(rows, cols, scale)#
{ r, newstate } = rndExp(rows, cols, scale, state)
Parameters:
• rows (scalar) – number of rows of resulting matrix.

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

• scale (scalar or matrix) – scalar or matrix that is ExE conformable with the dimensions of the output. The scale parameter sometimes called $$\beta$$

• 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:
• r (rows x cols matrix) – exponentially distributed random numbers.

• newstate (Opaque vector) – the updated state.

## Remarks#

The properties of the pseudo-random numbers in x are specified in terms of the scale parameter sometimes called $$\beta$$. This is the reciprocal of the rate parameter which is sometimes called $$\lambda$$:

$\begin{split}E(x) = scale = \beta = 1/rate = 1/\lambda\\ Var(x) = scale^2 =\beta^2 = 1/rate^2 = 1/\lambda^2\end{split}$