rndChiSquare¶
Purpose¶
Creates pseudo-random numbers with a chi-squared distribution, with an optional non-centrality parameter and a choice of underlying random number generator.
Format¶
-
x =
rndChiSquare
(r, c, df[, s_ncp])¶ -
{ x, newstate } =
rndChiSquare
(r, c, df, s_ncp, state) - Parameters:
r (scalar) – number of rows of resulting matrix.
c (scalar) – number of columns of resulting matrix.
df (scalar) – degrees of freedom.
s_ncp (scalar) –
Optional argument, non-centrality parameter.
Note
This is the square root of the noncentrality parameter that sometimes goes under the symbol \(\lambda\).
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:
x (RxC matrix) – chi-square distributed random numbers.
newstate (Opaque vector) – the updated state.
Remarks¶
The properties of the pseudo-random numbers in x are:
\[ \begin{align}\begin{aligned}\begin{split}E(x) = k + \lambda\\\end{split}\\\sigma^2(x) = 2*k + 4*\lambda\end{aligned}\end{align} \]where:
\[ \begin{align}\begin{aligned}k = df\\\lambda = s\_ncp^2\end{aligned}\end{align} \]Technical Notes¶
The default generator for
rndChiSquare()
is the SFMT Mersenne-Twister 19937. You can specify a different underlying random number generator with the functionrndCreateState()
.See also
Functions
rndCreateState()
,rndStateSkip()