# 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.

##### Extends

Class "UnivariateDistribution", directly. Class "Distribution", by class "UnivariateDistribution".

##### 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")}

##### code

"AffLinDistribution"

##### 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.

##### concept

• absolutely continuous distribution
• S4 distribution class

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
• initialize,AbscontDistribution-method
• initialize,AffLinAbscontDistribution-method
##### 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 0.4379882.
p(A3)(0) # The (approximated) probability that x <= 0 is 0.4562021.
q(A3)(.1) # The (approximated) 10 percent quantile is 0.1.
Documentation reproduced from package distr, version 2.0.2, License: LGPL-3

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