PoweR (version 1.0.7)

law0023.GeneralizedPareto: The Generalized Pareto Distribution

Description

Random generation for the Generalized Pareto 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 0, respectively.

The Generalized Pareto distribution with parameters mu = \(\mu\), sigma = \(\sigma\) and xi = \(\xi\) has density: $$ \frac{1}{\sigma}\left(1+\frac{\xi(x-\mu)}{\sigma} \right)^{(-\frac{1}{\xi}-1)} $$ where \(x \ge \mu\) if \(\xi \ge 0\) and \(x \le \mu - \sigma/\xi\) if \(\xi < 0\).

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 Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(23,10000,law.pars=c(8,6,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }