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NAG[g05lec] NAG[nag_rngs_beta] - Generates a vector of random numbers from a  distribution, seeds and generator number passed explicitly
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Calling Sequence
g05lec(a, b, n, x, igen, iseed, 'fail'=fail)
nag_rngs_beta(. . .)
Parameters
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a - float;
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On entry:  , the argument of the beta distribution.
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Constraint:  . .
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b - float;
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On entry:  , the argument of the beta distribution.
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Constraint:  . .
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n - integer;
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On entry:  , the number of pseudo-random numbers to be generated.
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Constraint:  . .
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x - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array x must be at least  .
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On exit: the  pseudo-random numbers from the specified beta distribution.
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iseed - Vector(1.. , datatype=integer[kernelopts('wordsize')/8]);
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On entry: contains values which define the current state of the selected generator.
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On exit: contains updated values defining the new state of the selected generator.
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_rngs_beta (g05lec) generates a vector of pseudo-random numbers taken from a beta distribution with  and  .
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Description
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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, ]]](/support/helpjp/helpview.aspx?si=9888/file08497/math130.png)
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:
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If  , 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;
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One of the initialization functions g05kbc (nag_rngs_init_repeatable) (for a repeatable sequence if computed sequentially) or g05kcc (nag_rngs_init_nonrepeatable) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_beta (g05lec).
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Error Indicators and Warnings
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"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_INT"
On entry,  . Constraint:  .
"NE_INTERNAL_ERROR"
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.
"NE_REAL"
On entry,  . Constraint:  .
On entry,  . Constraint:  .
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Further Comments
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To generate an observation,  , from the beta distribution of the second kind from an observation,  , generated by nag_rngs_beta (g05lec) the transformation,  , may be used.
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Examples
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>
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a := 2:
b := 2:
n := 5:
igen := 1:
x := Vector(5, datatype=float[8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05lec(a, b, n, x, igen, iseed):
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See Also
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Atkinson A C (1979) A family of switching algorithms for the computer generation of beta random variates Biometrika 66 141–5
Cheng R C H (1978) Generating beta variates with nonintegral shape parameters Comm. ACM 21 317–322
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworths
g05 Chapter Introduction.
NAG Toolbox Overview.
NAG Web Site.
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