﻿ g05sh Method
g05sh generates a vector of pseudorandom numbers taken from an $F$ (or Fisher's variance ratio) distribution with $\mu$ and $\nu$ degrees of freedom.

# Syntax

C#
```public static void g05sh(
int n,
int df1,
int df2,
G05..::..G05State g05state,
double[] x,
out int ifail
)```
Visual Basic
```Public Shared Sub g05sh ( _
n As Integer, _
df1 As Integer, _
df2 As Integer, _
g05state As G05..::..G05State, _
x As Double(), _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void g05sh(
int n,
int df1,
int df2,
G05..::..G05State^ g05state,
array<double>^ x,
[OutAttribute] int% ifail
)```
F#
```static member g05sh :
n : int *
df1 : int *
df2 : 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: ${\mathbf{n}}\ge 0$.
df1
Type: System..::..Int32
On entry: $\mu$, the number of degrees of freedom of the distribution.
Constraint: ${\mathbf{df1}}\ge 1$.
df2
Type: System..::..Int32
On entry: $\nu$, the number of degrees of freedom of the distribution.
Constraint: ${\mathbf{df2}}\ge 1$.
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 $F$-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)
 $fx=μ+ν-22!x12μ-112μ-1!12ν-1!1+μνx12μ+ν×μν12μif ​x>0,fx=0otherwise.$
g05sh calculates the values
 $νyiμzi, i=1,2,…,n,$
where ${y}_{i}$ and ${z}_{i}$ are generated by g05sj from gamma distributions with parameters $\left(\frac{1}{2}\mu ,2\right)$ and $\left(\frac{1}{2}\nu ,2\right)$ respectively (i.e., from ${\chi }^{2}$-distributions with $\mu$ and $\nu$ 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 g05sh.

# 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, ${\mathbf{df1}}<1$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{df2}}<1$.
${\mathbf{ifail}}=4$
 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 g05sh increases with $\mu$ and $\nu$.