Pseudo-random real numbers from the beta distribution

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NAG[g05fec] NAG[nag_random_beta] - Pseudo-random real numbers from the beta distribution

Calling Sequence

g05fec(a, b, x, 'n'=n, 'fail'=fail)

nag_random_beta(. . .)

Parameters

a - float;

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

Constraint: . .

b - float;

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

Constraint: . .

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

On exit: the pseudo-random variates from the specified beta 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_beta (g05fec) generates a vector of pseudo-random variates from a beta distribution with arguments and .

Description

The beta distribution has PDF (probability density function):

[[f(x)=(GAMMA(a,+,b))/(GAMMA(a)GAMMA(b))x^(a-1)(1,-,x)^(b-1), 0<=x<=1&;a,b>0.0],[f(x)=0, ]]

One of four algorithms is used to generate the variates depending on the values of and . Let be the maximum and be the minimum of and . Then the algorithms are as follows:

Jöhnk's algorithm is used, see for example Dagpunar (1988). This generates the beta variate as , where and are uniformly distributed random variates.

The algorithm BB given by Cheng (1978) is used. This involves the generation of an observation from a beta distribution of the second kind by the envelope rejection method using a log-logistic target distribution and then transforming it to a beta variate.

If and

The switching algorithm given by Atkinson (1979) is used. The two target distributions used are and , along with the approximation to the switching argument of .

In all other cases

Cheng's BC algorithm, see Cheng (1978), is used with modifications suggested by Dagpunar (1988). This algorithm is similar to BB, used when , but is tuned for small values of and .

	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 beta distribution of the second kind from an observation, , generated by nag_random_beta (g05fec) the transformation, , may be used. To generate an observation, , from an -distribution with degrees of freedom and generate an observation from the beta distribution with arguments and and use the transformation .