Pseudo-random real numbers from the gamma distribution

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NAG[g05ffc] NAG[nag_random_gamma] - Pseudo-random real numbers from the gamma distribution

Calling Sequence

g05ffc(a, b, x, 'n'=n, 'fail'=fail)

nag_random_gamma(. . .)

Parameters

a - float;

On entry: the argument, , of the gamma distribution.

Constraint: . .

b - float;

On entry: the argument, , of the gamma distribution.

Constraint: . .

x - Vector(1..n, datatype=float[8]);

On exit: the pseudo-random variates from the specified gamma distribution.

'n'=n - integer; (optional)

Default value: the first dimension of the array x.

On entry: the number, , of pseudo-random numbers to be generated

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_random_gamma (g05ffc) generates a vector of pseudo-random variates from a gamma distribution with arguments and .

Description

The gamma distribution has PDF (probability density function):

[[f(x)=1/(b^aGAMMA(a))x^(a-1)e^(-x/b), x>=0&;a,b>0],[f(x)=0, ]]

One of three algorithms is used to generate the variates depending upon the value of :

If a switching algorithm described by Dagpunar (1988) (called G6), is used. The target distributions are and , where , and the switching argument, , is taken as . This is similar to GS algorithm of Ahrens and Dieter (1974) in which .

If the gamma distribution reduces to the exponential distribution and the method based on the logarithmic transformation of a uniform random variate is used.

If the algorithm given by Best (1978) is used. This is based on using a Student's -distribution with two degrees of freedom as the target distribution in an envelope rejection method.

	Error Indicators and Warnings
	"NE_INT_ARG_LE" On entry, n must not be less than or equal to 0: . "NE_REAL_ARG_LE" On entry, a must not be less than or equal to 0.0: .

	Accuracy
	Not applicable.

Further Comments

To generate an observation from the distribution with degrees of freedom generate an observation from a gamma distribution with arguments , .

To generate an observation, , from a Student's -distribution with degrees of freedom generate an observation, , from a gamma distribution with arguments and and an observation, , from a standard Normal distribution (see g05ddc (nag_random_normal)) and use the transformation .