NAG Library Function Document
nag_rngs_compd_poisson (g05mec) generates a vector of pseudorandom integers, each from a discrete Poisson distribution with differing parameter .
||nag_rngs_compd_poisson (Integer m,
const double vlamda,
nag_rngs_compd_poisson (g05mec) generates
, each from a discrete Poisson distribution with mean
, where the probability of
The methods used by this function have low set up times and are designed for efficient use when the value of the parameter
changes during the simulation. For large samples from a distribution with fixed
using nag_rngs_poisson (g05mkc)
to set up and use a reference vector may be more efficient.
the product of uniforms method is used, see for example Dagpunar (1988)
. For larger values of
an envelope rejection method is used with a target distribution:
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
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).
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
m – IntegerInput
, the number of Poisson distributions for which pseudorandom variates are required.
vlamda[m] – const doubleInput
On entry: the means, , for , of the Poisson distributions.
is the largest integer representable on the machine (see nag_max_integer (X02BBC)
x[m] – IntegerOutput
On exit: the pseudorandom numbers from the specified Poisson distributions.
igen – IntegerInput
: 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)
iseed – 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.
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, .
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, for at least one value of .
On entry, at least one element of .
This example prints ten pseudorandom integers from five Poisson distributions with means
. 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
9.3 Program Results
Program Results (g05mece.r)