AbscontDistributionclass
Class "AbscontDistribution"
The AbscontDistribution
class is the motherclass 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.
 Keywords
 distribution
Objects from the Class
Objects can be created by calls of the form 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.
Slots
img
 Object of class
"Reals"
: the space of the image of this distribution which has dimension 1 and the name "Real Space" param
 Object of class
"Parameter"
: the parameter of this distribution, having only the slot name "Parameter of an absolutely continuous distribution" r
 Object of class
"function"
: generates random numbers d
 Object of class
"function"
: density function p
 Object of class
"function"
: cumulative distribution function q
 Object of class
"function"
: quantile function gaps
 [from version 1.9 on] Object of class
"OptionalMatrix"
, i.e.; an object which may either beNULL
oramatrix
. This slot, if nonNULL
, contains left and right endpoints of intervals where the density of the object is 0. This slot may be inspected by the accessorgaps()
and modified by a corresponding replacement method. It may also be filled automatically bysetgaps()
. For saved objects from earlier versions, we provide functionsisOldVersion
andconv2NewVersion
. .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 "UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.
Methods
 initialize
signature(.Object = "AbscontDistribution")
: initialize method Math
signature(x = "AbscontDistribution")
: application of a mathematical function, e.g.sin
orexp
(does not work withlog
,sign
!), to this absolutely continouos distribution
abs
:signature(x = "AbscontDistribution")
: exact image distribution ofabs(x)
. 
exp
:signature(x = "AbscontDistribution")
: exact image distribution ofexp(x)
. 
sign
:signature(x = "AbscontDistribution")
: exact image distribution ofsign(x)
. 
sqrt
:signature(x = "AbscontDistribution")
: exact image distribution ofsqrt(x)
. 
log
:signature(x = "AbscontDistribution")
: (with optional further argumentbase
, defaulting toexp(1)
) exact image distribution oflog(x)
. 
log10
:signature(x = "AbscontDistribution")
: exact image distribution oflog10(x)
. 
gamma
:signature(x = "AbscontDistribution")
: exact image distribution ofgamma(x)
. 
lgamma
:signature(x = "AbscontDistribution")
: exact image distribution oflgamma(x)
. 
digamma
:signature(x = "AbscontDistribution")
: exact image distribution ofdigamma(x)
. 
sqrt
:signature(x = "AbscontDistribution")
: exact image distribution ofsqrt(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. plot
signature(object = "AbscontDistribution")
: plots density, cumulative distribution and quantile function.
Internal subclass "AffLinAbscontDistribution"
To enhance accuracy of several functionals on distributions,
mainly from package distrEx, from version 1.9 of this package on,
there is an internally used (but exported) subclass
"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.
Internal virtual superclass "AcDcLcDistribution"
As many operations should be valid no matter whether the operands
are of class "AbscontDistribution"
,
"DiscreteDistribution"
, or "UnivarLebDecDistribution"
,
there is a class union of these classes called "AcDcLcDistribution"
;
in partiucalar methods for "*"
, "/"
,
"^"
(see operatorsmethods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.
See Also
AbscontDistribution
Parameterclass
UnivariateDistributionclass
Betaclass
Cauchyclass
Chisqclass
Expclass
Fdclass
Gammadclass
Lnormclass
Logisclass
Normclass
Tdclass
Unifclass
Weibullclass
DiscreteDistributionclass
Realsclass
RtoDPQ
Examples
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.