nag_rand_poisson (g05tjc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_poisson (g05tjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_poisson (g05tjc) generates a vector of pseudorandom integers from the discrete Poisson distribution with mean λ.

2  Specification

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

3  Description

nag_rand_poisson (g05tjc) 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 λ0.
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_poisson (g05tjc) 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_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_poisson (g05tjc).

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:     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_poisson (g05tjc).
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:     lambdadoubleInput
On entry: λ, the mean of the Poisson distribution.
Constraint: lambda0.0.
4:     r[lr]doubleCommunication Array
On entry: if mode=Nag_GenerateFromReference, the reference vector from the previous call to nag_rand_poisson (g05tjc).
If mode=Nag_GenerateWithoutReference, r is not referenced by nag_rand_poisson (g05tjc).
On exit: the reference vector.
5:     lrIntegerInput
On entry: the dimension of the array r.
Suggested values:
  • if modeNag_GenerateWithoutReference, lr=30+20×lambda+lambda;
  • otherwise lr=1.
Constraints:
  • if mode=Nag_InitializeReference or Nag_InitializeAndGenerate,
    • if lambda>7.15, lr>9+int8.5+14.3×lambda;
    • otherwise lr>9+intlambda+7.15×lambda+8.5;
  • if mode=Nag_GenerateFromReference, lr must remain unchanged from the previous call to nag_rand_poisson (g05tjc).
6:     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.
7:     x[n]IntegerOutput
On exit: the n pseudorandom numbers from the specified Poisson distribution.
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_INT
On entry, lr is too small when mode=Nag_InitializeReference or Nag_InitializeAndGenerate: lr=value, minimum length required =value.
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
lambda is not the same as when r was set up in a previous call.
Previous value of lambda=value and lambda=value.
NE_REAL
lambda is such that lr would have to be larger than the largest representable integer. Use mode=Nag_GenerateWithoutReference instead. lambda=value.
On entry, lambda=value.
Constraint: lambda0.0.
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 10 pseudorandom integers from a Poisson distribution with mean λ=20, generated by a single call to nag_rand_poisson (g05tjc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05tjce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05tjce.r)


nag_rand_poisson (g05tjc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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