law0011.Weibull {PoweR} | R Documentation |
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)
.
Author(s)
P. Lafaye de Micheaux, V. A. Tran
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
res <- gensample(11,10000,law.pars=c(8,6))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)