g05te generates a vector of pseudorandom integers from the discrete hypergeometric distribution of the number of specified items in a sample of size

l

, taken from a population of size

k

with

m

specified items in it.

Syntax

C#
public static void g05te( int mode, int n, int ns, int np, int m, double[] r, G05..::..G05State g05state, int[] x, out int ifail )

Visual Basic
Public Shared Sub g05te ( _ mode As Integer, _ n As Integer, _ ns As Integer, _ np As Integer, _ m As Integer, _ r As Double(), _ g05state As G05..::..G05State, _ x As Integer(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual Basic

Public Shared Sub g05te ( _
	mode As Integer, _
	n As Integer, _
	ns As Integer, _
	np As Integer, _
	m As Integer, _
	r As Double(), _
	g05state As G05..::..G05State, _
	x As Integer(), _
	<OutAttribute> ByRef ifail As Integer _
)

Visual C++
public: static void g05te( int mode, int n, int ns, int np, int m, array<double>^ r, G05..::..G05State^ g05state, array<int>^ x, [OutAttribute] int% ifail )

F#
static member g05te : mode : int * n : int * ns : int * np : int * m : int * 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 g05te.
$mode = 2$: 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: $n \geq 0$ .

ns: Type: System..::..Int32
On entry: $l$ , the sample size of the hypergeometric distribution.

Constraint: $0 \leq ns \leq np$ .

np: Type: System..::..Int32
On entry: $k$ , the population size of the hypergeometric distribution.

Constraint: $np \geq 0$ .

m: Type: System..::..Int32
On entry: $m$ , the number of specified items of the hypergeometric distribution.

Constraint: $0 \leq m \leq np$ .

r: Type: array<System..::..Double>[]()[][]
An array of size [lr]
On entry: if $mode = 1$ , the reference vector from the previous call to g05te.
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 pseudorandom numbers from the specified hypergeometric 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

g05te generates

n

integers

x_{i}

from a discrete hypergeometric distribution, where the probability of

x_{i} = I

\begin{matrix} P (i = I) = \frac{l! m! (k - l)! (k - m)!}{I! (l - I)! (m - I)! (k - m - l + I)! k!} & if I = \max (0, m + l - k), \dots, \min (l, m), \\ P (i = I) = 0 & otherwise. \end{matrix}

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 g05te with the same parameter values can then use this reference vector to generate further variates. The reference array is generated by a recurrence relation if

l m (k - l) (k - m) < 50 k^{3}

, otherwise Stirling's approximation is used.

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 g05te.

References

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,	$ns > np$ ,
or	$ns < 0$ .

$ifail = 4$: On entry, $np < 0$ .

$ifail = 5$

On entry,	$m > np$ ,
or	$m < 0$ .

$ifail = 6$: On entry, at least one of ns, np or m is not the same as when r was set up in a previous call to g05te with $mode = 0$ or $2$ .
On entry, the r vector was not initialized correctly or has been corrupted.