law0028.GeneralizedExtValue {PoweR} | R Documentation |
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.
Author(s)
P. Lafaye de Micheaux, V. A. Tran
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
res <- gensample(28,10000,law.pars=c(8,6,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)