nag_rand_neg_bin (g05thc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rand_neg_bin (g05thc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_neg_bin (g05thc) generates a vector of pseudorandom integers from the discrete negative binomial distribution with parameter m and probability p of success at a trial.

2  Specification

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

3  Description

nag_rand_neg_bin (g05thc) generates n integers xi from a discrete negative binomial distribution, where the probability of xi=I (I successes before m failures) is
Pxi=I= m+I-1! I!m-1! ×pI×1-pm,  I=0,1,.
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_neg_bin (g05thc) with the same parameter value can then use this reference vector to generate further variates.
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_neg_bin (g05thc).

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_neg_bin (g05thc).
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:     mIntegerInput
On entry: m, the number of failures of the distribution.
Constraint: m0.
4:     pdoubleInput
On entry: p, the parameter of the negative binomial distribution representing the probability of success at a single trial.
Constraint: 0.0p<1.0.
5:     r[lr]doubleCommunication Array
On entry: if mode=Nag_GenerateFromReference, the reference vector from the previous call to nag_rand_neg_bin (g05thc).
If mode=Nag_GenerateWithoutReference, r is not referenced by nag_rand_neg_bin (g05thc).
On exit: the reference vector.
6:     lrIntegerInput
On entry: the dimension of the array r.
Suggested values:
  • if modeNag_GenerateWithoutReference,
    lr=28+ 20× m×p +30×p / 1-p ​ approximately ;
  • otherwise lr=1.
  • if mode=Nag_InitializeReference or Nag_InitializeAndGenerate,
    lr> int m×p+7.15 × m×p+ 20.15×p 1-p +8.5 - max 0,int m× p-7.15 × m×p 1-p +9 ;
  • if mode=Nag_GenerateFromReference, lr must remain unchanged from the previous call to nag_rand_neg_bin (g05thc).
7:     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.
8:     x[n]IntegerOutput
On exit: the n pseudorandom numbers from the specified negative binomial distribution.
9:     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, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
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.
p or m is not the same as when r was set up in a previous call.
Previous value of p=value and p=value.
Previous value of m=value and m=value.
On entry, p=value.
Constraint: 0.0p<1.0.
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


9  Example

This example prints 20 pseudorandom integers from a negative binomial distribution with parameters m=60 and p=0.999, generated by a single call to nag_rand_neg_bin (g05thc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05thce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05thce.r)

nag_rand_neg_bin (g05thc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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