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.
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_neg_bin (g05thc).
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:     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.
Constraints:
  • 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

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, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
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
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.
NE_REAL
On entry, p=value.
Constraint: 0.0p<1.0.
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

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

None.

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