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

# Syntax

C#
```public static void g05sn(
int n,
int df,
G05..::.G05State g05state,
double[] x,
out int ifail
)```
Visual Basic (Declaration)
```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: n0.
df
Type: System..::.Int32
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df1 .
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: ifail=0 unless the method detects an error (see [Error Indicators and Warnings]).

# Description

The distribution has PDF (probability density function)
 fx= ν-12 ! 12ν-1!πν 1+x2ν 12ν+1 .
g05sn calculates the values
 yiνzi,   i= 1,…,n
where the yi are generated by g05sk from a Normal distribution with mean 0 and variance 1.0, and the zi are generated by g05sj from a gamma distribution with parameters 12ν and 2 (i.e., from a χ2-distribution with ν degrees of freedom).