g05sd generates a vector of pseudorandom numbers taken from a χ2-distribution with ν degrees of freedom.

Syntax

C#
public static void g05sd(
	int n,
	int df,
	G05..::..G05State g05state,
	double[] x,
	out int ifail
)
Visual Basic
Public Shared Sub g05sd ( _
	n As Integer, _
	df As Integer, _
	g05state As G05..::..G05State, _
	x As Double(), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g05sd(
	int n, 
	int df, 
	G05..::..G05State^ g05state, 
	array<double>^ x, 
	[OutAttribute] int% ifail
)
F#
static member g05sd : 
        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: n≥0.
df
Type: System..::..Int32
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df≥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 χ2-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=xν/2-1×e-x/22ν/2×ν/2-1!if ​x>0;fx=0otherwise.
This is the same as a gamma distribution with parameters ν/2 and 2.
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 g05sd.

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:
ifail=1
On entry, n<0.
ifail=2
On entry, df<1.
ifail=3
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 g05sd increases with ν.

Example

See Also