nag_rngs_hypergeometric (g05mlc) (PDF version)
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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.
mode=0
Set up reference vector only.
mode=1
Generate variates using reference vector set up in a prior call to nag_rngs_hypergeometric (g05mlc).
mode=2
Set up reference vector and generate variates.
mode=3
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

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, mode=value.
Constraint: mode=0, 1, 2 or 3.
On entry, n=value.
Constraint: n1.
On entry, np=value.
Constraint: np0.
NE_INT_2
On entry, m=value and np=value.
Constraint: mnp and m0.
On entry, ns=value and np=value.
Constraint: nsnp and ns0.
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.

7  Accuracy

Not applicable.

8  Further Comments

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)

9.2  Program Data

None.

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