PoweR (version 1.0.7)

law0028.GeneralizedExtValue: The Generalized Extreme Value Distribution

Description

Random generation for the Generalized Extreme Value distribution with parameters mu, sigma and xi.

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

Details

If mu, sigma and xi are not specified they assume the default values of 0, 1 and 1, respectively.

The Generalized Extreme Value distribution with parameters mu = \(\mu\), sigma = \(\sigma\) and xi = \(\xi\) has density: $$ [1+z]_{+}^{-\frac{1}{\xi}-1}\exp\left\{-[1+z]_{+}^{-\frac{1}{\xi}}\right\}/\sigma $$ for \(\xi > 0\) or \(\xi < 0\), where \(z = \xi (x - \mu)/\sigma\). If \(\xi = 0\), PDF is as same as in the Gumbel distribution.

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 law0026.Gumbel for the Gumbel distribution. See Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(28,10000,law.pars=c(8,6,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }