# 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 function rndCreateState().