NAG Library Function Document

nag_rand_binomial (g05tac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{mode}$ – Nag_ModeRNGInput

On entry: a code for selecting the operation to be performed by the function.

$\mathbf{mode}=\mathrm{Nag\_InitializeReference}$

Set up reference vector only.

$\mathbf{mode}=\mathrm{Nag\_GenerateFromReference}$

Generate variates using reference vector set up in a prior call to nag_rand_binomial (g05tac).

$\mathbf{mode}=\mathrm{Nag\_InitializeAndGenerate}$

Set up reference vector and generate variates.

$\mathbf{mode}=\mathrm{Nag\_GenerateWithoutReference}$

Generate variates without using the reference vector.

Constraint: $\mathbf{mode}=\mathrm{Nag\_InitializeReference}$, $\mathrm{Nag\_GenerateFromReference}$, $\mathrm{Nag\_InitializeAndGenerate}$ or $\mathrm{Nag\_GenerateWithoutReference}$.

2:    $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 0$.

3:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of trials of the distribution.

Constraint: $\mathbf{m}\ge 0$.

4:    $\mathbf{p}$ – doubleInput

On entry: $p$, the probability of success of the binomial distribution.

Constraint: $0.0\le \mathbf{p}\le 1.0$.

5:    $\mathbf{r}\left[\mathbf{lr}\right]$ – doubleCommunication Array

On entry: if $\mathbf{mode}=\mathrm{Nag\_GenerateFromReference}$, the reference vector from the previous call to nag_rand_binomial (g05tac).

If $\mathbf{mode}=\mathrm{Nag\_GenerateWithoutReference}$, r is not referenced and may be NULL.

On exit: if $\mathbf{mode}\ne \mathrm{Nag\_GenerateWithoutReference}$, the reference vector.

6:    $\mathbf{lr}$ – IntegerInput

On entry: the dimension of the array r.

Suggested values:

• if $\mathbf{mode}\ne \mathrm{Nag\_GenerateWithoutReference}$, $\mathbf{lr}=22+20\times \sqrt{\mathbf{m}\times \mathbf{p}\times \left(1-\mathbf{p}\right)}$;
• otherwise $\mathbf{lr}=1$.

Constraints:

• if $\mathbf{mode}=\mathrm{Nag\_InitializeReference}$ or $\mathrm{Nag\_InitializeAndGenerate}$,
  $\begin{array}{lll}\mathbf{lr}& >& \min \left(\mathbf{m},\mathrm{int}\left[\mathbf{m}\times \mathbf{p}+7.15\times \sqrt{\mathbf{m}\times \mathbf{p}\times \left(1-\mathbf{p}\right)}+1\right]\right)\\ & & -\max \left(0,\mathrm{int}\left[\mathbf{m}\times \mathbf{p}-7.15\times \sqrt{\mathbf{m}\times \mathbf{p}\times \left(1-\mathbf{p}\right)}-7.15\right]\right)+8\end{array}$;
• if $\mathbf{mode}=\mathrm{Nag\_GenerateFromReference}$, lr must remain unchanged from the previous call to nag_rand_binomial (g05tac).

7:    $\mathbf{state}\left[\mathit{dim}\right]$ – IntegerCommunication Array

Note: the dimension, $\mathit{dim}$, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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.

8:    $\mathbf{x}\left[\mathbf{n}\right]$ – IntegerOutput

On exit: the $n$ pseudorandom numbers from the specified binomial distribution.

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, lr is too small when $\mathbf{mode}=\mathrm{Nag\_InitializeReference}$ or $\mathrm{Nag\_InitializeAndGenerate}$: $\mathbf{lr}=〈\mathit{\text{value}}〉$, minimum length required $=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

NE_INTERNAL_ERROR

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 for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_STATE

On entry, state vector has been corrupted or not initialized.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_PREV_CALL

p or m is not the same as when r was set up in a previous call.
Previous value of $\mathbf{p}=〈\mathit{\text{value}}〉$ and $\mathbf{p}=〈\mathit{\text{value}}〉$.
Previous value of $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.

NE_REAL

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $0.0\le \mathbf{p}\le 1.0$.

NE_REF_VEC

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

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05tace.c)

10.2

Program Data

10.3

Program Results

Program Results (g05tace.r)