Weibull-class {distr} | R Documentation |
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
:"Reals"
: The space of the image of this distribution has got dimension 1
and the name "Real Space". param
:"WeibullParameter"
: the parameter of this distribution (shape and scale),
declared at its instantiation r
:"function"
: generates random numbers (calls function rweibull
)d
:"function"
: density function (calls function dweibull
)p
:"function"
: cumulative function (calls function pweibull
)q
:"function"
: inverse of the cumulative function (calls function qweibull
)
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/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 statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.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. shape(W) # shape of this distribution is 1. shape(W) <- 2 # shape of this distribution is now 2.