# 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 the rndKM 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.

randkm.src