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.

Examples#

// Set seed for repeatable output
rndseed 12345;

// Generate a 3x2 matrix of Weibull
// random numbers with shape = 2, scale = 1
x = rndWeibull(3, 2, 2, 1);
print x;

After the code above, x is:

0.31622572       0.89932217
0.52063284        1.4300231
0.82098160        1.6673537

See also

Functions rndCreateState(), rndStateSkip()

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