AbscontDistribution
-class is the mother-class of the classes Beta
, Cauchy
,
Chisq
, Exp
, F
, Gammad
, Lnorm
, Logis
, Norm
, T
, Unif
and
Weibull
. Further absolutely continuous distributions can be defined either by declaration of
own random number generator, density, cumulative distribution and quantile functions, or as result of a
convolution of two absolutely continuous distributions or by application of a mathematical operator to an absolutely
continuous distribution.new("AbscontDistribution", r, d, p, q)
.
More comfortably, you may use the generating function AbscontDistribution
.
The result of these calls is an absolutely continuous distribution.img
"Reals"
: the space of the image of this distribution which has dimension 1
and the name "Real Space" param
"Parameter"
: the parameter of this distribution, having only
the slot name "Parameter of an absolutely continuous distribution" r
"function"
: generates random numbersd
"function"
: density functionp
"function"
: cumulative distribution functionq
"function"
: quantile functiongaps
"OptionalMatrix"
,
i.e.; an object which may either be NULL
ora matrix
.
This slot, if non-NULL
, contains left and right
endpoints of intervals where the density of the object is 0. This slot
may be inspected by the accessor gaps()
and modified by a corresponding
replacement method. It may also be filled automatically by
setgaps()
. For saved objects from earlier versions, we provide functions
isOldVersion
and conv2NewVersion
..withArith
.withSim
.logExact
.lowerExact
Symmetry
"DistributionSymmetry"
;
used internally to avoid unnecessary calculations."UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.signature(.Object = "AbscontDistribution")
: initialize method signature(x = "AbscontDistribution")
: application of a mathematical function, e.g. sin
or
exp
(does not work with log
, sign
!), to this absolutely continouos distribution
abs
: signature(x = "AbscontDistribution")
: exact image distribution of abs(x)
.
exp
: signature(x = "AbscontDistribution")
: exact image distribution of exp(x)
.
sign
: signature(x = "AbscontDistribution")
: exact image distribution of sign(x)
.
sqrt
: signature(x = "AbscontDistribution")
: exact image distribution of sqrt(x)
.
log
: signature(x = "AbscontDistribution")
: (with optional further argument base
, defaulting to exp(1)
) exact image distribution of log(x)
.
log10
: signature(x = "AbscontDistribution")
: exact image distribution of log10(x)
.
gamma
: signature(x = "AbscontDistribution")
: exact image distribution of gamma(x)
.
lgamma
: signature(x = "AbscontDistribution")
: exact image distribution of lgamma(x)
.
digamma
: signature(x = "AbscontDistribution")
: exact image distribution of digamma(x)
.
sqrt
: signature(x = "AbscontDistribution")
: exact image distribution of sqrt(x)
.
signature(e1 = "AbscontDistribution")
: application of `-' to this absolutely continuous distribution.signature(e1 = "AbscontDistribution", e2 = "numeric")
: multiplication of this absolutely continuous distribution by an object of class "numeric"
signature(e1 = "AbscontDistribution", e2 = "numeric")
: division of this absolutely continuous distribution by an object of class "numeric"
signature(e1 = "AbscontDistribution", e2 = "numeric")
: addition of this absolutely continuous distribution to an object of class "numeric"
.signature(e1 = "AbscontDistribution", e2 = "numeric")
: subtraction of an object of class "numeric"
from this absolutely continuous distribution.signature(e1 = "numeric", e2 = "AbscontDistribution")
: multiplication of this absolutely continuous distribution by an object of class "numeric"
.signature(e1 = "numeric", e2 = "AbscontDistribution")
: addition of this absolutely continuous distribution to an object of class "numeric"
.signature(e1 = "numeric", e2 = "AbscontDistribution")
: subtraction of this absolutely continuous distribution from an object of class "numeric"
.signature(e1 = "AbscontDistribution", e2 = "AbscontDistribution")
: Convolution of two absolutely continuous distributions. The slots p, d and q are approximated by grids.signature(e1 = "AbscontDistribution", e2 = "AbscontDistribution")
: Convolution of two absolutely continuous distributions. The slots p, d and q are approximated by grids.signature(object = "AbscontDistribution")
: plots density, cumulative distribution and quantile function."AffLinAbscontDistribution"
which has extra slots
a
, b
(both of class "numeric"
), and X0
(of class "AbscontDistribution"
), to capture the fact
that the object has the same distribution as a * X0 + b
. This is
the class of the return value of methods
signature(e1 = "AbscontDistribution")
signature(e1 = "AbscontDistribution", e2 = "numeric")
signature(e1 = "AbscontDistribution", e2 = "numeric")
signature(e1 = "AbscontDistribution", e2 = "numeric")
signature(e1 = "AbscontDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "AbscontDistribution")
signature(e1 = "numeric", e2 = "AbscontDistribution")
signature(e1 = "numeric", e2 = "AbscontDistribution")
signature(e1 = "AffLinAbscontDistribution")
signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")
signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")
signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")
signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "AffLinAbscontDistribution")
signature(e1 = "numeric", e2 = "AffLinAbscontDistribution")
signature(e1 = "numeric", e2 = "AffLinAbscontDistribution")
"AffLinAbscontDistribution"
,
"AffLinDiscreteDistribution"
, "AffLinUnivarLebDecDistribution"
and called "AffLinDistribution"
which is used for functionals."AbscontDistribution"
,
"DiscreteDistribution"
, or "UnivarLebDecDistribution"
,
there is a class union of these classes called "AcDcLcDistribution"
;
in partiucalar methods for "*"
, "/"
,
"^"
(see operators-methods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.AbscontDistribution
Parameter-class
UnivariateDistribution-class
Beta-class
Cauchy-class
Chisq-class
Exp-class
Fd-class
Gammad-class
Lnorm-class
Logis-class
Norm-class
Td-class
Unif-class
Weibull-class
DiscreteDistribution-class
Reals-class
RtoDPQ
N <- Norm() # N is a normal distribution with mean=0 and sd=1.
E <- Exp() # E is an exponential distribution with rate=1.
A1 <- E+1 # a new absolutely continuous distributions with exact slots d, p, q
A2 <- A1*3 # a new absolutely continuous distributions with exact slots d, p, q
A3 <- N*0.9 + E*0.1 # a new absolutely continuous distribution with approximated slots d, p, q
r(A3)(1) # one random number generated from this distribution, e.g. -0.7150937
d(A3)(0) # The (approximated) density for x=0 is 0.43799.
p(A3)(0) # The (approximated) probability that x <= 0 is 0.45620.
q(A3)(.1) # The (approximated) 10 percent quantile is -1.06015.
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