﻿ g05sn Method
g05sn generates a vector of pseudorandom numbers taken from a Student's $t$-distribution with $\nu$ degrees of freedom.

# Syntax

C#
```public static void g05sn(
int n,
int df,
G05..::..G05State g05state,
double[] x,
out int ifail
)```
Visual Basic
```Public Shared Sub g05sn ( _
n As Integer, _
df As Integer, _
g05state As G05..::..G05State, _
x As Double(), _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void g05sn(
int n,
int df,
G05..::..G05State^ g05state,
array<double>^ x,
[OutAttribute] int% ifail
)```
F#
```static member g05sn :
n : int *
df : int *
g05state : G05..::..G05State *
x : float[] *
ifail : int byref -> unit
```

#### Parameters

n
Type: System..::..Int32
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
df
Type: System..::..Int32
On entry: $\nu$, the number of degrees of freedom of the distribution.
Constraint: ${\mathbf{df}}\ge 1$.
g05state
Type: NagLibrary..::..G05..::..G05State
An Object of type G05.G05State.
x
Type: array<System..::..Double>[]()[][]
An array of size [n]
On exit: the $n$ pseudorandom numbers from the specified Student's $t$-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

The distribution has PDF (probability density function)
 $fx=ν-12!12ν-1!πν1+x2ν12ν+1.$
g05sn calculates the values
 $yiνzi, i=1,…,n$
where the ${y}_{i}$ are generated by g05sk from a Normal distribution with mean $0$ and variance $1.0$, and the ${z}_{i}$ are generated by g05sj from a gamma distribution with parameters $\frac{1}{2}\nu$ and $2$ (i.e., from a ${\chi }^{2}$-distribution with $\nu$ degrees of freedom).
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 g05sn.

# References

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, ${\mathbf{n}}<0$.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{df}}<1$.
${\mathbf{ifail}}=3$
 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.

# Parallelism and Performance

None.

The time taken by g05sn increases with $\nu$.