# rbeta: The Beta Random Number Generating Function In rBeta2009: The Beta Random Number and Dirichlet Random Vector Generating Functions

## Description

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

## Usage

 `1` ``` 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.

## Details

The beta distribution with parameters `shape1` = a and `shape2` = b has density

Γ(a+b)/(Γ(a)Γ(b)) x^(a-1)(1-x)^(b-1)

for a > 0, b > 0 and 0 ≤ x ≤ 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.

## Value

`rbeta` generates beta random numbers.

## Author(s)

Ching-Wei Cheng <[email protected]>,
Ying-Chao Hung <[email protected]>,
Narayanaswamy Balakrishnan <[email protected]>

## 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.

## 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.

`rbeta` in package stats.
 ```1 2``` ``` library(rBeta2009) rbeta(10, 0.7, 1.5) ```