rndLCn

Purpose

Returns a matrix of standard normal (pseudo) random variables and the state of the random number generator.

Note

This function is deprecated–use rndn()–but remains for backward compatibility.

Format

{ y, newstate } = rndLCn(r, c, state)

Parameters:

• r (scalar) – row dimension.

• c (scalar) – column dimension.

• state (scalar or vector) –

  scalar case

  state = starting seed value only. System default values are used for the additive and multiplicative constants.

  The defaults are 1013904223, and 1664525, respectively. These may be changed with Format and Format.

  If state = -1, GAUSS computes the starting seed based on the system clock.

  3x1 vector case

  [1]	the starting seed, uses the system clock if -1
  [2]	the multiplicative constant
  [3]	the additive constant

  4x1 vector case

  state = the state vector returned from a previous call to one of the rndLC random number generators.

Returns:

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

• newstate (4x1 vector) –

  [1]	the updated seed
  [2]	the multiplicative constant
  [3]	the additive constant
  [4]	the original initialization seed

Examples

state = 13;
n = 2000000000;
k = 1000000;
c = 0;
submean = {};

do while c < n;
   { y, state } = rndLCn(k, 1, state);
   submean = submean | meanc(y);
   c = c + k;
endo;

mean = meanc(submean);
print mean;

Remarks

r and c will be truncated to integers if necessary.

Technical Notes

The normal random number generator is based on the uniform random number generator, using the fast acceptance-rejection algorithm proposed by Kinderman, A.J. and J.G. Ramage, “Computer Generation of Normal Random Numbers,” Journal of the American Statistical Association, December 1976, Volume 71, Number 356, pp. 893-896. This algorithm calls the linear congruential uniform random number generator multiple times for each normal random number generated.

See rndLCu() for a description of the uniform random number generator algorithm.

See also

Functions rndLCu(), rndLCi(), rndcon(), rndmult()