nag_rand_hypergeometric (g05tec) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_rand_hypergeometric (g05tec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_hypergeometric (g05tec) 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.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_hypergeometric (Nag_ModeRNG mode, Integer n, Integer ns, Integer np, Integer m, double r[], Integer lr, Integer state[], Integer x[], NagError *fail)

3  Description

nag_rand_hypergeometric (g05tec) generates n integers xi from a discrete hypergeometric distribution, where the probability of xi=I is
Pi=I= l!m!k-l!k-m! I!l-I!m-I!k-m-l+I!k!   if  I = max0,m+l-k , , 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_rand_hypergeometric (g05tec) 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 lmk-lk-m<50k3, otherwise Stirling's approximation is used.
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_hypergeometric (g05tec).

4  References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5  Arguments

1:     modeNag_ModeRNGInput
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_rand_hypergeometric (g05tec).
Set up reference vector and generate variates.
Generate variates without using the reference vector.
Constraint: mode=Nag_InitializeReference, Nag_GenerateFromReference, Nag_InitializeAndGenerate or Nag_GenerateWithoutReference.
2:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     nsIntegerInput
On entry: l, the sample size of the hypergeometric distribution.
Constraint: 0nsnp.
4:     npIntegerInput
On entry: k, the population size of the hypergeometric distribution.
Constraint: np0.
5:     mIntegerInput
On entry: m, the number of specified items of the hypergeometric distribution.
Constraint: 0mnp.
6:     r[lr]doubleCommunication Array
On entry: if mode=Nag_GenerateFromReference, the reference vector from the previous call to nag_rand_hypergeometric (g05tec).
If mode=Nag_GenerateWithoutReference, r is not referenced and may be NULL.
On exit: if modeNag_GenerateWithoutReference, the reference vector.
7:     lrIntegerInput
On entry: the dimension of the array r.
Suggested values:
  • if modeNag_GenerateWithoutReference, lr = 28+20× ns×m× np-m × np-ns / np3  approximately;
  • otherwise lr=1.
  • if mode=Nag_InitializeReference or Nag_InitializeAndGenerate, lr must not be too small, but the limit is too complicated to specify;
  • if mode=Nag_GenerateFromReference, lr must remain unchanged from the previous call to nag_rand_hypergeometric (g05tec).
8:     state[dim]IntegerCommunication Array
Note: the dimension, dim, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
9:     x[n]IntegerOutput
On exit: the pseudorandom numbers from the specified hypergeometric distribution.
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, lr is too small when mode=Nag_InitializeReference or Nag_InitializeAndGenerate: lr=value, minimum length required =value.
On entry, n=value.
Constraint: n0.
On entry, np=value.
Constraint: np0.
On entry, m=value and np=value.
Constraint: 0mnp.
On entry, ns=value and np=value.
Constraint: 0nsnp.
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.
On entry, state vector has been corrupted or not initialized.
The value of ns, np or m is not the same as when r was set up in a previous call with mode=Nag_InitializeReference or Nag_InitializeAndGenerate.
On entry, some of the elements of the array r have been corrupted or have not been initialized.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments


10  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_rand_hypergeometric (g05tec), after initialization by nag_rand_init_repeatable (g05kfc).

10.1  Program Text

Program Text (g05tece.c)

10.2  Program Data


10.3  Program Results

Program Results (g05tece.r)

nag_rand_hypergeometric (g05tec) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014