Weibull-class

0th

Percentile

Class "Weibull"

The Weibull distribution with shape parameter $a$, by default $=1$, and scale parameter $b$ 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 $p(x) = 1 - exp(- (x/b)^a)$, the mean is $E(X) = b Gamma(1 + 1/a)$, and the $ Var(X) = b^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.

Slots

img
Object of class "Reals": The space of the image of this distribution has got dimension 1 and the name "Real Space".
param
Object of class "WeibullParameter": the parameter of this distribution (shape and scale), declared at its instantiation
r
Object of class "function": generates random numbers (calls function rweibull)
d
Object of class "function": density function (calls function dweibull)
p
Object of class "function": cumulative function (calls function pweibull)
q
Object of class "function": inverse of the cumulative function (calls function qweibull)
.withArith
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim
logical: used internally to issue warnings as to accuracy
.logExact
logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExact
logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetry
object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

Extends

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

Methods

initialize
signature(.Object = "Weibull"): initialize method
scale
signature(object = "Weibull"): returns the slot scale of the parameter of the distribution
scale<-
signature(object = "Weibull"): modifies the slot scale of the parameter of the distribution
shape
signature(object = "Weibull"): returns the slot shape of the parameter of the distribution
shape<-
signature(object = "Weibull"): modifies the slot shape of the parameter of the distribution
*
signature(e1 = "Weibull", e2 = "numeric"): For the Weibull distribution we use its closedness under positive scaling transformations.

See Also

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 2.6, License: LGPL-3

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