rndKMgam¶
Purpose¶
Computes Gamma pseudo-random numbers.
Format¶
-
{ x, newstate } =
rndKMgam
(r, c, alpha, state)¶ Parameters: - r (scalar) – number of rows of resulting matrix.
- c (scalar) – number of columns of resulting matrix.
- alpha (matrix or vector or scalar) – Shape argument for gamma distribution. ExE conformable with the row and column dimensions of the return matrix, r and c.
- state (scalar or 500x1 vector) –
scalar case
state = starting seed value only. If -1, GAUSS computes the starting seed based on the system clock.500x1 vector case
state = the state vector returned from a previous call to one of therndKM
random number functions.
Returns: - x (RxC matrix) – Gamma distributed random numbers.
- newstate (500x1 vector) – the updated state.
Remarks¶
The properties of the pseudo-random numbers in x are:
\[\begin{split}E(x) = \alpha\\
Var(x) = \alpha\\
x > 0\\
\alpha > 0\end{split}\]
To generate gamma(alpha, theta)
pseudo-random numbers where theta is a
scale parameter, multiply the result of rndKMgam()
by theta.
Thus
z = theta * rndgam(1, 1, alpha);
has the properties
\[\begin{split}E(z) = \alpha * \theta\\
Var(z) = \alpha * \theta^2\\
z > 0\\
\alpha > 0\\
\theta > 0\end{split}\]
r and c will be truncated to integers if necessary.
Technical Notes¶
rndKMgam()
uses the recur-with-carry KISS+Monster algorithm described in the rndKMi()
Technical Notes.
Source¶
randkm.src