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rBeta2009 (version 1.0)

rbeta: The Beta Random Number Generating Function

Description

Random generation for the beta distribution with parameters shape1 and shape2.

Usage

rbeta(n, shape1, shape2)

Arguments

n
Number of beta random numbers to generate. If length(n) > 1, the length is taken to be the number required.
shape1, shape2
Positive shape parameters.

Value

rbeta generates beta random numbers.

Source

rbeta uses a C translation of Y. C. Hung and N. Balakrishnan and Y. T. Lin (2009), Evaluation of beta generation algorithms, Communications in Statistics - Simulation and Computation, 38:750--770.

Details

The beta distribution with parameters shape1$ = a$ and shape2$ = b$ has density $$\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} x^{a-1} (1-x)^{b-1}$$ for $a > 0, b > 0$ and $0 \le x \le 1$. The mean is $a/(a+b)$ and the variance is $ab/((a+b)^2 (a+b+1))$. rbeta basically utilizes the following guideline primarily proposed by Hung et al. (2009) for generating beta random numbers.
  • When $max($shape1$, $shape2$) < 1$, the B00 algorithm (Sakasegawa, 1983) is used;
  • When shape1$ < 1 < $shape2 or shape1$ > 1 > $shape2, the B01 algorithm (Sakasegawa, 1983) is used;
  • When $min($shape1$, $shape1$) > 1$, the B4PE algorithm (Schmeiser and Babu, 1980) is used if one papameter is close to 1 and the other is large (say $> 4$); otherwise, the BPRS algorithm (Zechner and Stadlober, 1993) is used.

References

Y. C. Hung and N. Balakrishnan and Y. T. Lin (2009), Evaluation of beta generation algorithms, Communications in Statistics - Simulation and Computation, 38, 750--770. H. Sakasegawa (1983), Stratified rejection and squeeze method for generating beta random numbers, Annals of the Institute Statistical Mathematics, 35, 291--302. B.W. Schmeiser and A.J.G. Babu (1980), Beta variate generation via exponential majorizing functions, Operations Research, 28, 917--926. H. Zechner and E. Stadlober (1993), Generating beta variates via patchwork rejection, Computing, 50, 1--18.

See Also

rbeta in package stats.

Examples

Run this code
 library(rBeta2009)
 rbeta(10, 0.7, 1.5)

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