g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rngs_hypergeometric (g05mlc)

## 1  Purpose

nag_rngs_hypergeometric (g05mlc) 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 $n$ with $m$ specified items in it.

## 2  Specification

 #include #include
 void nag_rngs_hypergeometric (Integer mode, Integer ns, Integer np, Integer m, Integer n, Integer x[], Integer igen, Integer iseed[], double r[], NagError *fail)

## 3  Description

nag_rngs_hypergeometric (g05mlc) generates a vector of integers, ${x}_{i}$, from a discrete hypergeometric distribution, where the probability of ${x}_{i}=I$ is
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_hypergeometric (g05mlc) 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 $lm\left(n-l\right)\left(n-m\right)<50{n}^{3}$, otherwise Stirling's approximation is used.
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_hypergeometric (g05mlc).

## 4  References

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_hypergeometric (g05mlc).
${\mathbf{mode}}=2$
Set up reference vector and generate variates.
${\mathbf{mode}}=3$
Generate variates without using the reference vector.
Constraint: ${\mathbf{mode}}=0$, $1$, $2$ or $3$.
2:     nsIntegerInput
On entry: $l$, the sample size of the hypergeometric distribution.
Constraint: $0\le {\mathbf{ns}}\le {\mathbf{np}}$.
3:     npIntegerInput
On entry: $n$, the population size of the hypergeometric distribution.
Constraint: ${\mathbf{np}}\ge 0$.
4:     mIntegerInput
On entry: $m$, the number of specified items of the hypergeometric distribution.
Constraint: $0\le {\mathbf{m}}\le {\mathbf{np}}$.
5:     nIntegerInput
On entry: the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 1$.
6:     x[n]IntegerOutput
On exit: the pseudorandom numbers from the specified hypergeometric distribution.
7:     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).
8:     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.
9:     r[$\mathit{dim}$]doubleCommunication Array
Note: the dimension, dim, of the array r must be at least $20+20×\sqrt{\left({\mathbf{ns}}×{\mathbf{m}}×\left({\mathbf{np}}-{\mathbf{m}}\right)×\left({\mathbf{np}}-{\mathbf{ns}}\right)\right)/{{\mathbf{np}}}^{3}}$.
On entry: if ${\mathbf{mode}}=1$, the reference vector from the previous call to nag_rngs_hypergeometric (g05mlc).
On exit: the reference vector.
10:   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_INT
On entry, ${\mathbf{mode}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{mode}}=0$, $1$, $2$ or $3$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.
On entry, ${\mathbf{np}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{np}}\ge 0$.
NE_INT_2
On entry, ${\mathbf{m}}=〈\mathit{\text{value}}〉$ and ${\mathbf{np}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m}}\le {\mathbf{np}}$ and ${\mathbf{m}}\ge 0$.
On entry, ${\mathbf{ns}}=〈\mathit{\text{value}}〉$ and ${\mathbf{np}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{ns}}\le {\mathbf{np}}$ and ${\mathbf{ns}}\ge 0$.
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
ns or np or m is not the same as when r was set up in a previous call or the data in r has been corrupted.

Not applicable.

None.

## 9  Example

The example program prints $20$ pseudorandom integers from a hypergeometric distribution with $l=500$, $m=900$ and $n=1000$, generated by a single call to nag_rngs_hypergeometric (g05mlc), after initialization by nag_rngs_init_repeatable (g05kbc).

### 9.1  Program Text

Program Text (g05mlce.c)

None.

### 9.3  Program Results

Program Results (g05mlce.r)