Weibull-class | R Documentation |
The Weibull distribution with shape
parameter a
, by default =1
, and
scale
parameter \sigma
has density given by, by default =1
,
d(x) = (a/\sigma) {(x/\sigma)}^{a-1} \exp (-{(x/\sigma)}^{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"
.
signature(.Object = "Weibull")
: initialize method
signature(object = "Weibull")
: returns the slot scale
of the parameter of the distribution
signature(object = "Weibull")
: modifies the slot scale
of the parameter of the distribution
signature(object = "Weibull")
: returns the slot shape
of the parameter of the distribution
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/\sigma)}^a)
,
the mean is E(X) = \sigma \Gamma(1 + 1/a)
,
and the Var(X) = \sigma^2(\Gamma(1 + 2/a)-(\Gamma(1 + 1/a))^2)
.
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
WeibullParameter-class
AbscontDistribution-class
Reals-class
rweibull
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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