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NAG C Library Manual

NAG Library Function Document

nag_rngs_hypergeometric (g05mlc)

+ Contents

    1  Purpose
    7  Accuracy

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 <nag.h>
#include <nagg05.h>
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, xi, from a discrete hypergeometric distribution, where the probability of xi=I is
Pi=I= l!m!n-l!n-m! I!l-I!m-I!n-m-l+I!n!   if  I = max0,m+l-n , , minl,m , Pi=I=0   otherwise.
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 lmn-ln-m<50n3, 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.
Set up reference vector only.
Generate variates using reference vector set up in a prior call to nag_rngs_hypergeometric (g05mlc).
Set up reference vector and generate variates.
Generate variates without using the reference vector.
Constraint: mode=0, 1, 2 or 3.
2:     nsIntegerInput
On entry: l, the sample size of the hypergeometric distribution.
Constraint: 0nsnp.
3:     npIntegerInput
On entry: n, the population size of the hypergeometric distribution.
Constraint: np0.
4:     mIntegerInput
On entry: m, the number of specified items of the hypergeometric distribution.
Constraint: 0mnp.
5:     nIntegerInput
On entry: the number of pseudorandom numbers to be generated.
Constraint: n1.
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[dim]doubleCommunication Array
Note: the dimension, dim, of the array r must be at least 20+20×ns×m×np-m×np-ns/np3.
On entry: if 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 value had an illegal value.
On entry, mode=value.
Constraint: mode=0, 1, 2 or 3.
On entry, n=value.
Constraint: n1.
On entry, np=value.
Constraint: np0.
On entry, m=value and np=value.
Constraint: mnp and m0.
On entry, ns=value and np=value.
Constraint: nsnp and ns0.
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.
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.

7  Accuracy

Not applicable.

8  Further Comments


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)

9.2  Program Data


9.3  Program Results

Program Results (g05mlce.r)

nag_rngs_hypergeometric (g05mlc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012