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)
.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

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 2.1.1 Index]