R: Class "Weibull"

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

`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

### 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.
    ## 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.

[Package distr version 2.8.0 Index]