rndKMp#

Purpose#

Computes Poisson pseudo-random numbers.

Format#

{ x, newstate } = rndKMp(r, c, lambda, state)#
Parameters:

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

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

  • lambda (matrix or vector or scalar) – Shape argument for Poisson distribution, scalar or ExE conformable matrix with r and c.

  • state (scalar or 500x1 vector) –

    scalar case

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

    500x1 vector case

    state = the state vector returned from a previous call to one of the rndKM random number functions.

Returns:

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

  • newstate (500x1 vector) – the updated state.

Remarks#

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

\[\begin{split}E(x) = \lambda\\ Var(x) = \lambda\\ x = 0, 1,....\\ \lambda > 0\end{split}\]

r and c will be truncated to integers if necessary.

Examples#

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

The output is a 3x2 matrix of non-negative integers. The sample mean is approximately 5, consistent with the theoretical mean of lambda:

6.0000000        4.0000000
4.0000000        7.0000000
3.0000000        4.0000000

Technical Notes#

rndKMp() uses the recur-with-carry KISS+Monster algorithm described in the rndKMi() Technical Notes.

Source#

randkm.src

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