nag_rngs_binomial (g05mjc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rngs_binomial (g05mjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_binomial (g05mjc) generates a vector of pseudorandom integers from the discrete binomial distribution with parameters m and p.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_binomial (Integer mode, Integer m, double p, Integer n, Integer x[], Integer igen, Integer iseed[], double r[], NagError *fail)

3  Description

nag_rngs_binomial (g05mjc) generates n integers xi from a discrete binomial distribution, where the probability of xi=I is
Pxi=I= m! I!m-I! pI×1-pm-I,  I=0,1,,m,
where 0m and 0p1. This represents the probability of achieving I successes in m trials when the probability of success at a single trial is p.
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_binomial (g05mjc) with the same parameter values can then use this reference vector to generate further variates.
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_binomial (g05mjc).

4  References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
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.
Set up reference vector only.
Generate variates using reference vector set up in a prior call to nag_rngs_binomial (g05mjc).
Set up reference vector and generate variates.
Generate variates without using the reference vector.
Constraint: mode=0, 1, 2 or 3.
2:     mIntegerInput
On entry: m, the number of trials of the distribution.
Constraint: m0.
3:     pdoubleInput
On entry: p, the probability of success of the binomial distribution.
Constraint: 0.0p1.0.
4:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n1.
5:     x[n]IntegerOutput
On exit: the n pseudorandom numbers from the specified binomial distribution.
6:     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).
7:     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.
8:     r[dim]doubleCommunication Array
Note: the dimension, dim, of the array r must be at least
  • 22+20m×p1-p when mode=3;
  • 1 otherwise.
On entry: if mode=1, the reference vector from the previous call to nag_rngs_binomial (g05mjc).
If mode=3, r is not referenced by nag_rngs_binomial (g05mjc).
On exit: the reference vector.
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, m=value.
Constraint: m0.
On entry, mode=value.
Constraint: mode=0, 1, 2 or 3.
On entry, n=value.
Constraint: n1.
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.
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 p=value.
On entry, p<0.0 or p>1.0: p=value.

7  Accuracy

Not applicable.

8  Further Comments


9  Example

This example prints 20 pseudorandom integers from a binomial distribution with parameters m=6000 and p=0.8, generated by a single call to nag_rngs_binomial (g05mjc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05mjce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05mjce.r)

nag_rngs_binomial (g05mjc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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