naginterfaces.library.rand.int_poisson(mode, n, lamda, statecomm, comm=None)[source]

int_poisson generates a vector of pseudorandom integers from the discrete Poisson distribution with mean .

For full information please refer to the NAG Library document for g05tj


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 int_poisson.

Set up reference vector and generate variates.

Generate variates without using the reference vector.


, the number of pseudorandom numbers to be generated.


, the mean of the Poisson distribution.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

commNone or dict, communication object, optional, modified in place

Communication structure for the reference vector.

If , this argument must have been initialized by a prior call to int_poisson.

If , is not referenced and may be None.

xNone or int, ndarray, shape

The pseudorandom numbers from the specified Poisson distribution.

(errno )

On entry, .

Constraint: , , or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

is such that would have to be larger than the largest representable integer. Use instead. .

(errno )

is not the same as when [‘r’] was set up in a previous call.

Previous value of and .

(errno )

On entry, some of the elements of the array [‘r’] have been corrupted or have not been initialized.

(errno )

On entry, [‘state’] vector has been corrupted or not initialized.


int_poisson generates integers from a discrete Poisson distribution with mean , where the probability of is

where .

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 int_poisson 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 init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to int_poisson.


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