law0017.JohnsonSU {PoweR} | R Documentation |
The Johnson SU Distribution
Description
Random generation for the Johnson SU distribution with parameters mu
, sigma
, nu
and tau
.
This generator is called by function gensample
to create random variables based on its parameters.
Details
If mu
, sigma
, nu
and tau
are not specified they assume the default values of 0, 1, 0 and 0.5, respectively.
The Johnson SU distribution with parameters mu =
\mu
, sigma =
\sigma
, nu =
\nu
and tau =
\tau
has density:
\frac{1}{c\sigma\tau}\frac{1}{\sqrt{z^2+1}}\frac{1}{\sqrt{2\pi}}e^{-r^2/2}
where r = -\nu + (1/\tau)sinh^-1(z)
,
z = (x - (\mu + c*\sigma (\sqrt(\omega)) sinh(w)))/(c*\sigma)
,
c = ((w-1)(w cosh(2\omega)+1)/2)^-1/2
,
w = e^(\tau^2)
and \omega = -\nu\tau
.
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 Distributions
for other standard distributions.
Examples
res <- gensample(17,10000,law.pars=c(9,8,6,0.5))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)