Runuran (version 0.21.0)

udweibull: UNU.RAN object for Weibull distribution

Description

Create UNU.RAN object for a Weibull (Extreme value type III) distribution with with parameters shape and scale. [Distribution] -- Weibull (Extreme value type III).

Usage

udweibull(shape, scale=1, lb=0, ub=Inf)

Arguments

shape

(strictly positive) shape parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.cont".

Details

The Weibull distribution with shape parameter $a$ and scale parameter $\sigma$ has density given by $$f(x) = (a/\sigma) {(x/\sigma)}^{a-1} \exp (-{(x/\sigma)}^{a})$$ for $x \ge 0$.

The domain of the distribution can be truncated to the interval (lb,ub).

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions, Volume 1. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 21, p. 628.

See Also

unuran.cont.

Examples

## Create distribution object for Weibull distribution
distr <- udweibull(shape=3)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)