Description Objects from the Class Slots Extends Methods Note Author(s) See Also Examples

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 can be created by calls of the form `Weibull(shape, scale)`

.
This object is a Weibull distribution.

`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.

Class `"AbscontDistribution"`

, directly.

Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.

Class `"Distribution"`

, by class `"AbscontDistribution"`

.

- 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.

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)*.

Thomas Stabla [email protected],

Florian Camphausen [email protected],

Peter Ruckdeschel [email protected],

Matthias Kohl [email protected]

`WeibullParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rweibull`

1 2 3 4 5 6 7 8 | ```
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.
``` |

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