PoweR (version 1.0.7)

law0021.SkewNormal: The Skew Normal Distribution

Description

Random generation for the Skew Normal distribution with parameters xi, omega^2 and alpha.

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

Details

If xi, omega^2 and alpha are not specified they assume the default values of 0, 1 and 0, respectively.

The Skew Normal distribution with parameters xi = \(\xi\), omega^2 = \(\omega^2\) and alpha = \(\alpha\) has density: $$ \left(\frac{2}{\omega}\right)\phi\left(\frac{x-\xi}{\omega}\right)\Phi\left(\alpha\left(\frac{x-\xi}{\omega}\right)\right) $$ where \(\phi(x)\) is the standard normal probability density function and \(\Phi(x)\) is its cumulative distribution function.

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 law0002.Normal for the Normal distribution. See Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(21,10000,law.pars=c(8,6,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }