Weibull-class {distr}R Documentation

Class "Weibull"

Description

The Weibull distribution with shape parameter a, by default =1, and scale parameter b has density given by, by default =1,

d(x) = (a/b) (x/b)^(a-1) exp(- (x/b)^a)

for x > 0.

C.f. rweibull

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)

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.

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).

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

See Also

WeibullParameter-class AbscontDistribution-class Reals-class rweibull

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.

[Package distr version 2.0.6 Index]