PoweR (version 1.0.7)

law0011.Weibull: The Weibull Distribution

Description

Random generation for the Weibull distribution with parameters shape and scale.

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

Details

If shape or scale are not specified they assume the default values of 1 and 1, respectively.

The Weibull distribution with shape parameter \(k\) and scale parameter \(\lambda\) has density given by $$ \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x/\lambda)^k} $$ for \(x > 0\). The cumulative distribution function is \(F(x) = 1 - e^(-(x/\lambda)^k)\) on \(x > 0\), the mean is \(E(X) = \lambda \Gamma(1 + 1/k)\), and the \(Var(X) = \lambda^2 * (\Gamma(1 + 2/k) - (\Gamma(1 + 1/k))^2)\).

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(11,10000,law.pars=c(8,6))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }