PoweR (version 1.0.7)

law0008.Student: The Student t Distribution

Description

Random generation for the Student t distribution with df degrees of freedom.

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

Details

If df is not specified it assumes the default value of 1.

The t distribution with df = k degrees of freedom has density: $$ (\sqrt{k\pi})^{-1}\frac{\Gamma\left(\frac{k+1}{2} \right)}{\Gamma\left(\frac{k}{2} \right)}\left(1+\frac{t^2}{k} \right)^{-\frac{k+1}{2}} $$ for all real x. It has mean 0 (for \(k > 1\)) and variance \(k/(k-2)\) (for \(k > 2\)).

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

Distributions for other standard distributions.

Examples

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