# AbscontDistribution-class

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##### Class "AbscontDistribution"

The 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.

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 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

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 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.

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")

There also is a class union of "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 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

##### Aliases
• AbscontDistribution-class
• AffLinDistribution-class
• AffLinAbscontDistribution-class
• sqrt,AbscontDistribution-method
• initialize,AbscontDistribution-method
• initialize,AffLinAbscontDistribution-method
• sqrt,AbscontDistribution-method
##### Examples
# NOT RUN {
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.
## in RStudio or Jupytier IRKernel, use q.l(.)(.) instead of q(.)(.)
# }
`
Documentation reproduced from package distr, version 2.8.0, License: LGPL-3

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