rndGumbel¶
Purpose¶
Computes Gumbel distributed random numbers with a choice of underlying random number generator.
Format¶
-
r =
rndGumbel
(rows, cols, location, scale)¶ -
{ r, newstate } =
rndGumbel
(rows, cols, location, scale, state) Parameters: - rows (scalar) – number of rows of resulting matrix.
- cols (scalar) – number of columns of resulting matrix.
- location (scalar or matrix) – location parameter, scalar or ExE conformable matrix with rows and cols
- scale (scalar or matrix) – scaler parameter, scalar or ExE conformable matrix with rows and cols
- 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) – Gumbel distributed random numbers.
- newstate (Opaque vector) – the updated state.
Remarks¶
This function uses the definition of the Gumbel distribution corresponding to the minimum extreme. The properties of the pseudo-random numbers in y are:
\[\begin{split}E(y) = location - \gamma*scale \approx\\
location - 0.5772*scale\\
\gamma = \text{Euler-Mascheroni constant}\\
Var(y) = \frac{(\pi*scale)^2}{6}\end{split}\]
r and c will be truncated to integers if necessary.
See also
Functions rndCreateState()
, rndStateSkip()