NAG Library Function Document

nag_rngs_poisson (g05mkc)

The variates can be generated with or without using a search table and index. If a search table is used then it is stored with the index in a reference vector and subsequent calls to nag_rngs_poisson (g05mkc) with the same parameter values can then use this reference vector to generate further variates. The reference array is found using a recurrence relation if

λ

is less than

50

and by Stirling's formula otherwise.

One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_poisson (g05mkc).

4 References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5 Arguments

1: mode – IntegerInput

On entry: a code for selecting the operation to be performed by the function.

$mode = 0$: Set up reference vector only.
$mode = 1$: Generate variates using reference vector set up in a prior call to nag_rngs_poisson (g05mkc).
$mode = 2$: Set up reference vector and generate variates.
$mode = 3$: Generate variates without using the reference vector.

Constraint:

mode = 0

1

2

3

2: lambda – doubleInput

On entry:

λ

, the mean of the Poisson distribution.

Constraint:

lambda \geq 0.0

3: n – IntegerInput

On entry:

n

, the number of pseudorandom numbers to be generated.

Constraint:

n \geq 1

4: x[n] – IntegerOutput

On exit: the

n

pseudorandom numbers from the specified Poisson distribution.

5: igen – IntegerInput

On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).

6: iseed[ $4$ ] – IntegerCommunication Array

On entry: contains values which define the current state of the selected generator.

On exit: contains updated values defining the new state of the selected generator.

7: r[ $22 + 20 \times \sqrt{lambda}$ ] – doubleCommunication Array

On entry: if

mode = 1

, the reference vector from the previous call to nag_rngs_poisson (g05mkc).

On exit: the reference vector.

8: fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_DIM_INFEASIBLE: lambda is so large that the reference vector length would exceed integer range. We recommend setting $mode = 3$ . $lambda = 〈value〉$ .
NE_INT: On entry, $mode = 〈value〉$ .
Constraint: $mode = 0$ , $1$ , $2$ or $3$ .; On entry, $n = 〈value〉$ .
Constraint: $n \geq 1$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_PREV_CALL: lambda has changed since r was set up in a previous call. Previous value of $lambda = 〈value〉$ and $lambda = 〈value〉$ .
NE_REAL: On entry, $lambda = 〈value〉$ .
Constraint: $lambda \geq 0.0$ .