PoweR (version 1.1.4)

law0026.Gumbel: The Gumbel Distribution

Description

Random generation for the Gumbel distribution with parameters mu and sigma.

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

Author

P. Lafaye de Micheaux, V. A. Tran

Details

If mu or sigma are not specified, they assume the default values of 1.

The Gumbel distribution with parameters mu = \(\mu\) and sigma = \(\sigma\) has density: $$ \frac{1}{\sigma}\exp\left\{-\exp\left[-\left(\frac{x-\mu}{\sigma}\right)\right]-\left(\frac{x-\mu}{\sigma}\right)\right\} $$

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 law0028.GeneralizedExtValue for the Generalized Extreme Value distribution. See Distributions for other standard distributions.

Examples

res <- gensample(26,10000,law.pars=c(9,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)