# rndMVt¶

## Purpose¶

Computes multivariate Student-t distributed random numbers given a covariance matrix.

## Format¶

r = rndMVt(num, cov, df)
{ r, newstate } = rndMVt(num, cov, df, state)
Parameters:
• num (scalar) – number of random vectors to create.

• cov (NxN matrix) – covariance matrix

• df (scalar) – degrees of freedom.

• 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:
• r (num x N matrix) – multivariate student-t distributed random numbers.

• newstate (Opaque vector) – the updated state.

## Examples¶

// Degrees of freedom
df = 8;

// Covariance matrix
sigma = {   1 0.3,
0.3   1 };

x = rndMVt(100, sigma, df);


## Remarks¶

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

\begin{align}\begin{aligned}\begin{split}E(x) = 0\\\end{split}\\Var(x) = \bigg(\frac{df}{df - 2}\bigg) * \sigma\end{aligned}\end{align}