PoweR (version 1.0.7)

law0017.JohnsonSU: 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 \(\omega = -\nu\tau\).

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(17,10000,law.pars=c(9,8,6,0.5))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }