PoweR (version 1.0.7)

law0004.Logistic: The Logistic Distribution

Description

Random generation for the Logistic distribution with parameters location and scale.

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

Details

If location or scale are omitted, they assume the default values of 0 and 1 respectively.

The Logistic distribution with location = \(\mu\) and scale = s has distribution function

$$ \frac{1}{1 + exp^{-\frac{(x-\mu)}{s}}} $$

and density

$$ \frac{exp^{-\frac{(x-\mu)}{s}}}{s(1+exp^{-\frac{(x-\mu)}{s}})^2} $$

It is a long-tailed distribution with mean \(\mu\) and variance \((\pi^2)/3 s^2\).

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

See function rlogis from package stats. See Distributions for other standard distributions.

Examples

# NOT RUN {
res <- gensample(4,10000,law.pars=c(9,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }