g05sj generates a vector of pseudorandom numbers taken from a gamma distribution with parameters a and b.

Syntax

C#
public static void g05sj(
	int n,
	double a,
	double b,
	G05..::..G05State g05state,
	double[] x,
	out int ifail
)
Visual Basic
Public Shared Sub g05sj ( _
	n As Integer, _
	a As Double, _
	b As Double, _
	g05state As G05..::..G05State, _
	x As Double(), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g05sj(
	int n, 
	double a, 
	double b, 
	G05..::..G05State^ g05state, 
	array<double>^ x, 
	[OutAttribute] int% ifail
)
F#
static member g05sj : 
        n : int * 
        a : float * 
        b : 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.
a
Type: System..::..Double
On entry: a, the parameter of the gamma distribution.
Constraint: a>0.0.
b
Type: System..::..Double
On entry: b, the parameter of the gamma distribution.
Constraint: b>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 gamma 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 gamma distribution has PDF (probability density function)
fx=1baΓaxa-1e-x/bif ​x≤0;  a,b>0fx=0otherwise.
One of three algorithms is used to generate the variates depending upon the value of a:
(i) if a<1, a switching algorithm described by Dagpunar (1988) (called G6) is used. The target distributions are f1x=caxa-1/ta and f2x=1-ce-x-t, where c=t/t+ae-t, and the switching parameter, t, is taken as 1-a. This is similar to Ahrens and Dieter's GS algorithm (see Ahrens and Dieter (1974)) in which t=1;
(ii) if a=1, the gamma distribution reduces to the exponential distribution and the method based on the logarithmic transformation of a uniform random variate is used;
(iii) if a>1, the algorithm given by Best (1978) is used. This is based on using a Student's t-distribution with two degrees of freedom as the target distribution in an envelope rejection method.
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 g05sj.

References

Ahrens J H and Dieter U (1974) Computer methods for sampling from gamma, beta, Poisson and binomial distributions Computing 12 223–46
Best D J (1978) Letter to the Editor Appl. Statist. 27 181
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

Error Indicators and Warnings

Errors or warnings detected by the method:
ifail=1
On entry, n<0.
ifail=2
On entry, a≤0.0.
ifail=3
On entry, b≤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