NAG Library Function Document
nag_rand_poisson (g05tjc) generates a vector of pseudorandom integers from the discrete Poisson distribution with mean .
||nag_rand_poisson (Nag_ModeRNG mode,
nag_rand_poisson (g05tjc) generates
from a discrete Poisson distribution with mean
, where the probability of
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 is less than 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).
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
mode – Nag_ModeRNGInput
: 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_rand_poisson (g05tjc).
- Set up reference vector and generate variates.
- Generate variates without using the reference vector.
, , or .
n – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
lambda – doubleInput
On entry: , the mean of the Poisson distribution.
r[lr] – doubleCommunication Array
, the reference vector from the previous call to nag_rand_poisson (g05tjc).
is not referenced by nag_rand_poisson (g05tjc).
On exit: the reference vector.
lr – IntegerInput
: the dimension of the array r
- if , ;
- otherwise .
- if or ,
- if , ;
- otherwise ;
- if , lr must remain unchanged from the previous call to nag_rand_poisson (g05tjc).
state – IntegerCommunication Array
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.
x[n] – IntegerOutput
On exit: the pseudorandom numbers from the specified Poisson distribution.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument had an illegal value.
On entry, lr
is too small when
, minimum length required
On entry, .
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
On entry, state
vector has been corrupted or not initialized.
is not the same as when r
was set up in a previous call.
Previous value of
is such that lr
would have to be larger than the largest
representable integer. Use
On entry, .
On entry, some of the elements of the array r
have been corrupted or have not been initialized.
This example prints
pseudorandom integers from a Poisson distribution with mean
, 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
9.3 Program Results
Program Results (g05tjce.r)