PoweR (version 1.0.7)

law0005.Gamma: The Gamma Distribution

Description

Random generation for the Gamma distribution with parameters shape and rate.

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

Details

If shape or rate are not specified they assume the default values of 2 and 1, respectively.

The Gamma distribution has density: $$ \frac{1}{b^a\Gamma(a)}x^{a-1}exp^{-x/b} $$ for \(x \ge 0\), a > 0 and b > 0; where \(a\) is the shape parameter and \(b\) is the rate parameter.

Here \(\Gamma(a)\) is the gamma function implemented by R and defined in its help.

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 rgamma from package stats. See. Distributions for other standard distributions. Type help(gamma) for additional information about the gamma function.

Examples

# NOT RUN {
res <- gensample(5,10000,law.pars=c(9,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }