g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rngs_poisson (g05mkc)

## 1  Purpose

nag_rngs_poisson (g05mkc) generates a vector of pseudorandom integers from the discrete Poisson distribution with mean $\lambda$.

## 2  Specification

 #include #include
 void nag_rngs_poisson (Integer mode, double lambda, Integer n, Integer x[], Integer igen, Integer iseed[], double r[], NagError *fail)

## 3  Description

nag_rngs_poisson (g05mkc) generates $n$ integers ${x}_{i}$ from a discrete Poisson distribution with mean $\lambda$, where the probability of ${x}_{i}=I$ is
 $Pxi=I= λI×e-λ I! , I=0,1,…,$
where $0\le \lambda$.
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 $\lambda$ 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:     modeIntegerInput
On entry: a code for selecting the operation to be performed by the function.
${\mathbf{mode}}=0$
Set up reference vector only.
${\mathbf{mode}}=1$
Generate variates using reference vector set up in a prior call to nag_rngs_poisson (g05mkc).
${\mathbf{mode}}=2$
Set up reference vector and generate variates.
${\mathbf{mode}}=3$
Generate variates without using the reference vector.
Constraint: ${\mathbf{mode}}=0$, $1$, $2$ or $3$.
On entry: $\lambda$, the mean of the Poisson distribution.
Constraint: ${\mathbf{lambda}}\ge 0.0$.
3:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 1$.
4:     x[n]IntegerOutput
On exit: the $n$ pseudorandom numbers from the specified Poisson distribution.
5:     igenIntegerInput
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[$22+20×\sqrt{{\mathbf{lambda}}}$]doubleCommunication Array
On entry: if ${\mathbf{mode}}=1$, the reference vector from the previous call to nag_rngs_poisson (g05mkc).
On exit: the reference vector.
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_DIM_INFEASIBLE
lambda is so large that the reference vector length would exceed integer range. We recommend setting ${\mathbf{mode}}=3$. ${\mathbf{lambda}}=〈\mathit{\text{value}}〉$.
NE_INT
On entry, ${\mathbf{mode}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{mode}}=0$, $1$, $2$ or $3$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.
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 ${\mathbf{lambda}}=〈\mathit{\text{value}}〉$ and ${\mathbf{lambda}}=〈\mathit{\text{value}}〉$.
NE_REAL
On entry, ${\mathbf{lambda}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{lambda}}\ge 0.0$.

Not applicable.

None.

## 9  Example

This example prints $10$ pseudorandom integers from a Poisson distribution with mean $\lambda =20$, generated by a single call to nag_rngs_poisson (g05mkc), after initialization by nag_rngs_init_repeatable (g05kbc).

### 9.1  Program Text

Program Text (g05mkce.c)

None.

### 9.3  Program Results

Program Results (g05mkce.r)