distr: Weibull-class – R documentation

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Weibull-class

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
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.

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@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de

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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
shape(W) # shape of this distribution is 1.
shape(W) <- 2 # shape of this distribution is now 2.

distr

Object Oriented Implementation of Distributions

v2.8.0

LGPL-3

Authors

Florian Camphausen [ctb] (contributed as student in the initial phase --2005), Matthias Kohl [aut, cph], Peter Ruckdeschel [cre, cph], Thomas Stabla [ctb] (contributed as student in the initial phase --2005), R Core Team [ctb, cph] (for source file ks.c/ routines 'pKS2' and 'pKolmogorov2x')

Initial release

2019-03-11