naginterfaces.library.rand.int_​poisson

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

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

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

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g05/g05tjf.html

Parameters

modeint

A code for selecting the operation to be performed by the function.

$mode=0$

Set up reference vector only.

$mode=1$

Generate variates using reference vector set up in a prior call to int_poisson.

$mode=2$

Set up reference vector and generate variates.

$mode=3$

Generate variates without using the reference vector.

nint

$n$, the number of pseudorandom numbers to be generated.

lamdafloat

$\lambda$, 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 $mode=1$, this argument must have been initialized by a prior call to int_poisson.

If $mode=3$, $comm$ is not referenced and may be None.

Returns

xNone or int, ndarray, shape $\left(n\right)$

The $n$ pseudorandom numbers from the specified Poisson distribution.

Raises

NagValueError

(errno $1$)

On entry, $mode=⟨value⟩$.

Constraint: $mode=0$, $1$, $2$ or $3$.

(errno $2$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $3$)

On entry, $lamda=⟨value⟩$.

Constraint: $lamda\ge 0.0$.

(errno $3$)

$lamda$ is such that $\text{lr}$ would have to be larger than the largest representable integer. Use $mode=3$ instead. $lamda=⟨value⟩$.

(errno $4$)

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

Previous value of $lamda=⟨value⟩$ and $lamda=⟨value⟩$.

(errno $4$)

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

(errno $6$)

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

Notes

int_poisson generates $n$ integers $x_i$ from a discrete Poisson distribution with mean $\lambda$, where the probability of $x_i=I$ is

$$P(x_i=I)=\frac{{\lambda }^I\times e^{-\lambda }}{I!}\text{,}I=0,1,\dots \text{,}$$

where $\lambda \ge 0$.

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 $\lambda$ is less than $50$ 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.

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