g05sc generates a vector of pseudorandom numbers from a Cauchy distribution with median a and semi-interquartile range b.

Syntax

C#
public static void g05sc(
	int n,
	double xmed,
	double semiqr,
	G05..::..G05State g05state,
	double[] x,
	out int ifail
)
Visual Basic
Public Shared Sub g05sc ( _
	n As Integer, _
	xmed As Double, _
	semiqr As Double, _
	g05state As G05..::..G05State, _
	x As Double(), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g05sc(
	int n, 
	double xmed, 
	double semiqr, 
	G05..::..G05State^ g05state, 
	array<double>^ x, 
	[OutAttribute] int% ifail
)
F#
static member g05sc : 
        n : int * 
        xmed : float * 
        semiqr : float * 
        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.
xmed
Type: System..::..Double
On entry: a, the median of the distribution.
semiqr
Type: System..::..Double
On entry: b, the semi-interquartile range of the distribution.
Constraint: semiqr≥0.0.
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 Cauchy 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=1πb1+x-ab2.
g05sc returns the value
a+b2y1-1y2,
where y1 and y2 are a pair of consecutive pseudorandom numbers from a uniform distribution over 0,1, such that
2y1-12+y22≤1.
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 g05sc.

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=3
On entry, semiqr<0.0.
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

None.

Example

See Also