# rndKMbeta¶

## Purpose¶

Computes beta pseudo-random numbers.

## Format¶

{ x, newstate } = rndKMbeta(r, c, a, b, state)
Parameters:
• r (scalar) – number of rows of resulting matrix.

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

• a (matrix or vector or scalar) – First shape argument for beta distribution. ExE conformable with the row and column dimensions of the return matrix, r and c.

• b (matrix or vector or scalar) – Second shape argument for beta 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) – Beta distributed random numbers.

• newstate (500x1 vector) – the updated state.

## Remarks¶

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

\begin{align}\begin{aligned}\begin{split}E(x) = \frac{a}{a+b}\\\end{split}\\\begin{split}Var(x) = \frac{a*b}{(a+b+1)*(a+b^2)}\\\end{split}\\\begin{split}0 < x < 1\\\end{split}\\\begin{split}a > 0\\\end{split}\\b > 0\end{aligned}\end{align}

r and c will be truncated to integers if necessary.

## Technical Notes¶

rndKMbeta() uses the recur-with-carry KISS+Monster algorithm described in the rndKMi() Technical Notes.

randkm.src