g05sh generates a vector of pseudorandom numbers taken from an F (or Fisher's variance ratio) distribution with μ and ν 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: n≥0.
df1
Type: System..::..Int32
On entry: μ, the number of degrees of freedom of the distribution.
Constraint: df1≥1.
df2
Type: System..::..Int32
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df2≥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: 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 yi and zi are generated by g05sj from gamma distributions with parameters 12μ,2 and 12ν,2 respectively (i.e., from χ2-distributions with μ and ν 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:
ifail=1
On entry, n<0.
ifail=2
On entry, df1<1.
ifail=3
On entry, df2<1.
ifail=4
On entry,state vector was not initialized or has been corrupted.
ifail=-9000
An error occured, see message report.
ifail=-8000
Negative dimension for array value
ifail=-6000
Invalid Parameters value

Accuracy

Not applicable.

Parallelism and Performance

None.

Further Comments

The time taken by g05sh increases with μ and ν.

Example

See Also