﻿ g05ta Method
g05ta generates a vector of pseudorandom integers from the discrete binomial distribution with parameters $m$ and $p$.

# Syntax

C#
```public static void g05ta(
int mode,
int n,
int m,
double p,
double[] r,
G05..::..G05State g05state,
int[] x,
out int ifail
)```
Visual Basic
```Public Shared Sub g05ta ( _
mode As Integer, _
n As Integer, _
m As Integer, _
p As Double, _
r As Double(), _
g05state As G05..::..G05State, _
x As Integer(), _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void g05ta(
int mode,
int n,
int m,
double p,
array<double>^ r,
G05..::..G05State^ g05state,
array<int>^ x,
[OutAttribute] int% ifail
)```
F#
```static member g05ta :
mode : int *
n : int *
m : int *
p : float *
r : float[] *
g05state : G05..::..G05State *
x : int[] *
ifail : int byref -> unit
```

#### Parameters

mode
Type: System..::..Int32
On entry: a code for selecting the operation to be performed by the method.
${\mathbf{mode}}=0$
Set up reference vector only.
${\mathbf{mode}}=1$
Generate variates using reference vector set up in a prior call to g05ta.
${\mathbf{mode}}=2$
Set up reference vector and generate variates.
${\mathbf{mode}}=3$
Generate variates without using the reference vector.
Constraint: ${\mathbf{mode}}=0$, $1$, $2$ or $3$.
n
Type: System..::..Int32
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
m
Type: System..::..Int32
On entry: $m$, the number of trials of the distribution.
Constraint: ${\mathbf{m}}\ge 0$.
p
Type: System..::..Double
On entry: $p$, the probability of success of the binomial distribution.
Constraint: $0.0\le {\mathbf{p}}\le 1.0$.
r
Type: array<System..::..Double>[]()[][]
An array of size [lr]
On entry: if ${\mathbf{mode}}=1$, the reference vector from the previous call to g05ta.
If ${\mathbf{mode}}=3$, r is not referenced.
On exit: if ${\mathbf{mode}}\ne 3$, the reference vector.
g05state
Type: NagLibrary..::..G05..::..G05State
An Object of type G05.G05State.
x
Type: array<System..::..Int32>[]()[][]
An array of size [n]
On exit: the $n$ pseudorandom numbers from the specified binomial distribution.
ifail
Type: System..::..Int32%
On exit: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

# Description

g05ta generates $n$ integers ${x}_{i}$ from a discrete binomial distribution, where the probability of ${x}_{i}=I$ is
 $Pxi=I=m!I!m-I!⁢pI×1-pm-I, I=0,1,…,m,$
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 g05ta with the same parameter values can then use this reference vector to generate further variates.
One of the initialization methods (G05KFF not in this release) (for a repeatable sequence if computed sequentially) or (G05KGF not in this release) (for a non-repeatable sequence) must be called prior to the first call to g05ta.

# 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

# Error Indicators and Warnings

Errors or warnings detected by the method:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{mode}}\ne 0$, $1$, $2$ or $3$.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{n}}<0$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{m}}<0$.
${\mathbf{ifail}}=4$
 On entry, ${\mathbf{p}}<0.0$, or ${\mathbf{p}}>1.0$.
${\mathbf{ifail}}=5$
On entry, m or p is not the same as when r was set up in a previous call to g05ta with ${\mathbf{mode}}=0$ or $2$.
On entry, the r vector was not initialized correctly or has been corrupted.
${\mathbf{ifail}}=6$
On entry, lr is too small when ${\mathbf{mode}}=0$ or $2$.
${\mathbf{ifail}}=7$
 On entry, state vector was not initialized or has been corrupted.
${\mathbf{ifail}}=-9000$
An error occured, see message report.
${\mathbf{ifail}}=-8000$
Negative dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$

Not applicable.

None.