nag_rngs_poisson (g05mkc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rngs_poisson (g05mkc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_poisson (g05mkc) generates a vector of pseudorandom integers from the discrete Poisson distribution with mean λ.

2  Specification

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

3  Description

nag_rngs_poisson (g05mkc) generates n integers xi from a discrete Poisson distribution with mean λ, where the probability of xi=I is
Pxi=I= λI×e-λ I! ,  I=0,1,,
where 0λ.
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_poisson (g05mkc) with the same parameter values can then use this reference vector to generate further variates. The reference array is found using a recurrence relation if λ is less than 50 and by Stirling's formula otherwise.
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_poisson (g05mkc).

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.
mode=0
Set up reference vector only.
mode=1
Generate variates using reference vector set up in a prior call to nag_rngs_poisson (g05mkc).
mode=2
Set up reference vector and generate variates.
mode=3
Generate variates without using the reference vector.
Constraint: mode=0, 1, 2 or 3.
2:     lambdadoubleInput
On entry: λ, the mean of the Poisson distribution.
Constraint: lambda0.0.
3:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n1.
4:     x[n]IntegerOutput
On exit: the n pseudorandom numbers from the specified Poisson distribution.
5:     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).
6:     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.
7:     r[22+20×lambda]doubleCommunication Array
On entry: if mode=1, the reference vector from the previous call to nag_rngs_poisson (g05mkc).
On exit: the reference vector.
8:     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_DIM_INFEASIBLE
lambda is so large that the reference vector length would exceed integer range. We recommend setting mode=3. lambda=value.
NE_INT
On entry, mode=value.
Constraint: mode=0, 1, 2 or 3.
On entry, n=value.
Constraint: n1.
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_PREV_CALL
lambda has changed since r was set up in a previous call. Previous value of lambda=value and lambda=value.
NE_REAL
On entry, lambda=value.
Constraint: lambda0.0.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example prints 10 pseudorandom integers from a Poisson distribution with mean λ=20, generated by a single call to nag_rngs_poisson (g05mkc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05mkce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05mkce.r)


nag_rngs_poisson (g05mkc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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