rndLCgam

Purpose

Computes Gamma pseudo-random numbers.

Note

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

Format

{ x, newstate } = rndLCgam(r, c, alpha, state)

Parameters:

• r (scalar) – number of rows of resulting matrix.

• c (scalar) – number of columns of resulting matrix.

• alpha (matrix, vector or scalar) – shape argument for gamma distribution, scalar or ExE conformable matrix with r and c.

• 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:

• x (RxC matrix) – gamma distributed random numbers.

• newstate (4x1 vector) –

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

Examples

// Generate a 3x2 matrix of gamma random numbers
// with shape alpha = 5, using a fixed seed for repeatable output
{ x, newstate } = rndLCgam(3, 2, 5, 12345);
print x;

The output is a 3x2 matrix of gamma-distributed values. The sample mean is approximately 5, consistent with the theoretical mean of alpha:

4.3270396        9.4093462
3.9689646        4.7393241
6.1082705        5.6436564

Technical Notes

This function uses a linear congruential method, discussed in Kennedy, W.J. Jr., and J.E. Gentle, Statistical Computing, Marcel Dekker, Inc. 1980, pp. 136-147. Each seed is generated from the preceding seed using the formula

\[new\_seed = (((a * seed) \% 2^{32})+ c) \% 2^{32}\]

where % is the mod operator and where a is the multiplicative constant and c is the additive constant.

Source

randlc.src