nag_rngs_compd_poisson (g05mec) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rngs_compd_poisson (g05mec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_compd_poisson (g05mec) generates a vector of pseudorandom integers, each from a discrete Poisson distribution with differing parameter λ.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_compd_poisson (Integer m, const double vlamda[], Integer x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

nag_rngs_compd_poisson (g05mec) generates m integers xj, each from a discrete Poisson distribution with mean λj, where the probability of xj=I is
Pxj=I= λjI×e-λj I! ,  I=0,1,,
where
0λj,   j= 1,2,,m.
The methods used by this function have low set up times and are designed for efficient use when the value of the parameter λ changes during the simulation. For large samples from a distribution with fixed λ using nag_rngs_poisson (g05mkc) to set up and use a reference vector may be more efficient.
When λ<7.5 the product of uniforms method is used, see for example Dagpunar (1988). For larger values of λ an envelope rejection method is used with a target distribution:
fx=13 if ​x1, fx=13x-3 otherwise.
This distribution is generated using a ratio of uniforms method. A similar approach has also been suggested by Ahrens and Dieter (1989). The basic method is combined with quick acceptance and rejection tests given by Maclaren (1990). For values of λ87 Stirling's approximation is used in the computation of the Poisson distribution function, otherwise tables of factorials are used as suggested by Maclaren (1990).
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_compd_poisson (g05mec).

4  References

Ahrens J H and Dieter U (1989) A convenient sampling method with bounded computation times for Poisson distributions Amer. J. Math. Management Sci. 1–13
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Maclaren N M (1990) A Poisson random number generator Personal Communication

5  Arguments

1:     mIntegerInput
On entry: m, the number of Poisson distributions for which pseudorandom variates are required.
Constraint: m1.
2:     vlamda[m]const doubleInput
On entry: the means, λj, for j=1,2,,m, of the Poisson distributions.
Constraint: 0.0vlamda[j]maxint/2.0, where maxint is the largest integer representable on the machine (see nag_max_integer (X02BBC)).
3:     x[m]IntegerOutput
On exit: the m pseudorandom numbers from the specified Poisson distributions.
4:     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).
5:     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.
6:     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, m=value.
Constraint: m1.
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_REAL_ARRAY_ELEM_CONS
On entry, 2×vlamda[i-1]>MAXINT for at least one value of i=1,2,,m.
On entry, at least one element of vlamda<0.0.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example prints ten pseudorandom integers from five Poisson distributions with means λ1=0.5, λ2=5, λ3=10, λ4=50 and λ5=100. These are generated by ten calls to nag_rngs_compd_poisson (g05mec), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05mece.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05mece.r)


nag_rngs_compd_poisson (g05mec) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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