# rndWeibull¶

## Purpose¶

Computes Weibull pseudo-random numbers with the choice of underlying random number generator.

## Format¶

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

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

• shape (matrix or vector or scalar) – shape parameter, ExE conformable matrix with r and c.

• scale (matrix or vector or scalar) – scale parameter, 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 (RxC matrix) – Weibull distributed random numbers.

• newstate (Opaque vector) – the updated state.

## Remarks¶

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

\begin{align}\begin{aligned}\begin{split}E(x) = scale * \Gamma(1 + 1/shape)\\\end{split}\\Var(x) = scale^2*( \Gamma(1 + \frac{2}{shape}) - (\Gamma(1 + \frac{1}{shape}))^2 )\end{aligned}\end{align}

r and c will be truncated to integers if necessary.