# rndn¶

## Purpose¶

Computes normally distributed pseudo-random numbers with a choice of underlying random number generator.

## Format¶

y = rndn(r, c)
{ y, newstate } = rndn(r, c, state)
Parameters
• r (scalar) – row dimension.

• c (scalar) – column dimension.

• 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
• y (RxC matrix) – standard normal random numbers.

• newstate (Opaque vector) – the updated state.

## Examples¶

### Example 1¶

//Create a 100 by 1 vector of standard normal numbers
my_var = rndn(100, 1);


### Example 2¶

This example simulates the linear model: $$y = \alpha + \beta_1*X + \epsilon$$

num_obs = 100;
alpha = 2.5;
beta_1 = 0.8;

// Simulate error term
err = rndn(num_obs, 1);

// Simulate 'x' variable
x = rndn(num_obs, 1);

// Simulate data generating process
y = alpha + beta_1*x + err;


### Example 3¶

This example generates two thousand vectors of standard normal random numbers, each with one million elements. The state of the random number generator after each iteration is used as an input to the next generation of random numbers.

state = 13;
n = 2000;
k = 1000000;

// Create vector to hold 'n' submeans
submean = zeros(n, 1);

for i(1, n, 1);
// Create a kx1 vector of random normal numbers,
// using the optional 'state' input
{ y, state } = rndn(k, 1, state);

submean[i] = meanc(y);
endfor;

mean = meanc(submean);
print mean;


## Remarks¶

r and c will be truncated to integers if necessary.

## Technical Notes¶

• The default generator for rndn() is the SFMT Mersenne-Twister 19937. You can specify a different underlying random number generator with the function rndCreateState().

• The rndseed keyword will create a new state vector (starting point) for rndn(). This means you can use rndseed to control rndn(). However, rndn() will not update the rndseed as its internal state changes.

• For testing and comparison purposes, the function _rndng10() will reproduce the results of the function rndn() in GAUSS 10 and earlier. In GAUSS 11 an improvement to the normality transformation algorithm was added to rndn(). This can be reproduced with the function _rndn(). Do not use either of the functions for any purpose other than comparison with previous versions. The current rndn() algorithm is a much higher quality random number generator.