AbscontDistribution-class {distr}R Documentation

Class "AbscontDistribution"

Description

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. An additional way is, to specify only the random number generator. The function RtoDPQ then approximates the three remaining slots d, p and q by random sampling.

Objects from the Class

Objects can be created by calls of the form new("AbscontDistribution", r, d, p, q). The result of this call 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.

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!), to this absolutely continouos distribution
-
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

There also is a class union of "AffLinAbscontDistribution" and "AffLinDiscreteDistribution" called "AffLinDistribution" which is used for functionals.

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@uni-bayreuth.de,
Matthias Kohl Matthias.Kohl@stamats.de

See Also

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

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.

[Package distr version 1.9 Index]