nag_rand_hypergeometric (g05tec) (PDF version)
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NAG C 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.
mode=Nag_InitializeReference
Set up reference vector only.
mode=Nag_GenerateFromReference
Generate variates using reference vector set up in a prior call to nag_rand_hypergeometric (g05tec).
mode=Nag_InitializeAndGenerate
Set up reference vector and generate variates.
mode=Nag_GenerateWithoutReference
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 by nag_rand_hypergeometric (g05tec).
On exit: 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.
Constraints:
  • 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 actual argument supplied must be the array state supplied to the initialization functions 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

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
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.
NE_INT_2
On entry, m=value and np=value.
Constraint: 0mnp.
On entry, ns=value and np=value.
Constraint: 0nsnp.
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_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_PREV_CALL
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.
NE_REF_VEC
On entry, some of the elements of the array r have been corrupted or have not been initialized.

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

9.1  Program Text

Program Text (g05tece.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05tece.r)


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

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