g05tj generates a vector of pseudorandom integers from the discrete Poisson distribution with mean

λ

Syntax

C#
public static void g05tj( int mode, int n, double lambda, double[] r, G05..::..G05State g05state, int[] x, out int ifail )

Visual Basic
Public Shared Sub g05tj ( _ mode As Integer, _ n As Integer, _ lambda As Double, _ r As Double(), _ g05state As G05..::..G05State, _ x As Integer(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void g05tj( int mode, int n, double lambda, array<double>^ r, G05..::..G05State^ g05state, array<int>^ x, [OutAttribute] int% ifail )

F#
static member g05tj : mode : int * n : int * lambda : float * r : float[] * g05state : G05..::..G05State * x : int[] * ifail : int byref -> unit

Parameters

mode

Type: System..::..Int32

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

$mode = 0$: Set up reference vector only.
$mode = 1$: Generate variates using reference vector set up in a prior call to g05tj.
$mode = 2$: Set up reference vector and generate variates.
$mode = 3$: Generate variates without using the reference vector.

Constraint:

mode = 0

1

2

3

n: Type: System..::..Int32
On entry: $n$ , the number of pseudorandom numbers to be generated.

Constraint: $n \geq 0$ .

lambda: Type: System..::..Double
On entry: $λ$ , the mean of the Poisson distribution.

Constraint: $lambda \geq 0.0$ .

r: Type: array<System..::..Double>[]()[][]
An array of size [lr]
On entry: if $mode = 1$ , the reference vector from the previous call to g05tj.
If $mode = 3$ , r is not referenced.

On exit: if $mode \neq 3$ , the reference vector.

g05state: Type: NagLibrary..::..G05..::..G05State
An Object of type G05.G05State.

x: Type: array<System..::..Int32>[]()[][]
An array of size [n]
On exit: the $n$ pseudorandom numbers from the specified Poisson distribution.

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

g05tj generates

n

integers

x_{i}

from a discrete Poisson distribution with mean

λ

, where the probability of

x_{i} = I

P (x_{i} = I) = \frac{λ^{I} \times e^{- λ}}{I!}, I = 0, 1, \dots,

where

λ \geq 0

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 g05tj 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 methods (G05KFF not in this release) (for a repeatable sequence if computed sequentially) or (G05KGF not in this release) (for a non-repeatable sequence) must be called prior to the first call to g05tj.

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

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$: On entry, $mode \neq 0$ , $1$ , $2$ or $3$ .

$ifail = 2$: On entry, $n < 0$ .

$ifail = 3$: On entry, $lambda < 0.0$ .
$mode = 0$ or $2$ and lambda is such that lr would have to be larger than the largest representable integer. Use $mode = 3$ in this case.

$ifail = 4$: On entry, lambda is not the same as when r was set up in a previous call to g05tj with $mode = 0$ or $2$ .
On entry, the r vector was not initialized correctly, or has been corrupted.