# Weibull-class

0th

Percentile

##### Class "Weibull"

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

Keywords
distribution
##### Note

The density is $d(x)=0$ for $x < 0$. The cumulative is $p(x) = 1 - \exp(-{(x/\sigma)}^a)$, the mean is $E(X) = \sigma \Gamma(1 + 1/a)$, and the $Var(X) = \sigma^2(\Gamma(1 + 2/a)-(\Gamma(1 + 1/a))^2)$.

##### Objects from the Class

Objects can be created by calls of the form Weibull(shape, scale). This object is a Weibull distribution.

##### Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

##### concept

• absolutely continuous distribution
• Weibull distribution
• S4 distribution class
• generating function

WeibullParameter-class AbscontDistribution-class Reals-class rweibull

##### Aliases
• Weibull-class
• Weibull
• initialize,Weibull-method
##### Examples
W <- Weibull(shape=1,scale=1) # W is a Weibull distribution with shape=1 and scale=1.
r(W)(1) # one random number generated from this distribution, e.g. 0.5204105
d(W)(1) # Density of this distribution is 0.3678794 for x=1.
p(W)(1) # Probability that x<1 is 0.6321206.
q(W)(.1) # Probability that x<0.1053605 is 0.1.
shape(W) # shape of this distribution is 1.
shape(W) <- 2 # shape of this distribution is now 2.
Documentation reproduced from package distr, version 2.0.6, License: LGPL-3

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