PoweR (version 1.0.7)

law0006.Beta: The Beta Distribution

Description

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

This generator is called by function gensample to create random variables based on its parameters.

Details

If shape1 or shape2 are not specified they assume the default values of 1 and 1, respectively.

The Beta distribution with parameters shape1 = a and shape2 = b has density: $$ \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha-1}(1-x)^{\beta-1} $$ for \(a > 0, b > 0\) and \(0 \le x \le 1\) where the boundary values at \(x=0\) or \(x=1\) are defined as by continuity (as limits).

References

Pierre Lafaye de Micheaux, Viet Anh Tran (2016). PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Studies for Goodness-of-fit Tests in R. Journal of Statistical Software, 69(3), 1--42. doi:10.18637/jss.v069.i03

See Also

See function rbeta from package stats. See Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(6,10000,law.pars=c(9,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }