naginterfaces.library.rand.int_​binomial

naginterfaces.library.rand.int_binomial(mode, n, m, p, statecomm, comm=None)

int_binomial generates a vector of pseudorandom integers from the discrete binomial distribution with parameters $m$ and $p$.

For full information please refer to the NAG Library document for g05ta

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g05/g05taf.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_binomial.

$mode=2$

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.

mint

$m$, the number of trials of the distribution.

pfloat

$p$, the probability of success of the binomial 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_binomial.

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 binomial 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, $m=⟨value⟩$.

Constraint: $m\ge 0$.

(errno $4$)

On entry, $p=⟨value⟩$.

Constraint: $0.0\le p\le 1.0$.

(errno $5$)

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

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

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

(errno $5$)

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

(errno $7$)

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

Notes

int_binomial generates $n$ integers $x_i$ from a discrete binomial distribution, where the probability of $x_i=I$ is

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

where $m\ge 0$ and $0\le p\le 1$. This represents the probability of achieving $I$ successes in $m$ trials when the probability of success at a single trial is $p$.

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_binomial with the same parameter values can then use this reference vector to generate further variates.

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_binomial.

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