Runuran (version 0.40)

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)

Value

An object of class "unuran.cont".

Arguments

shape

(strictly positive) shape parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

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)