Computes Gamma pseudo-random numbers.


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


{ x, newstate } = rndLCgam(r, c, alpha, state)
  • 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 rndcon and rndmult.

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

    3x1 vector case


    the starting seed, uses the system clock if -1


    the multiplicative constant


    the additive constant

    4x1 vector case

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

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

  • newstate (4x1 vector) –


    the updated seed


    the multiplicative constant


    the additive constant


    the original initialization seed

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.