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:     mode Nag_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:     n IntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     lambda doubleInput
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 and may be NULL.
On exit: if modeNag_GenerateWithoutReference, the reference vector.
5:     lr IntegerInput
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 dimension, dim, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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:     fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
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
Parallelism and Performance

nag_rand_poisson (g05tjc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9
Further Comments

None.

10
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).

10.1
Program Text

Program Text (g05tjce.c)

10.2
Program Data

None.

10.3
Program Results

Program Results (g05tjce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017