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 therndKM
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.
Source¶
randkm.src