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.
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.
imgObject of class "Reals": the space of the image of this distribution which has dimension 1
and the name "Real Space"
paramObject of class "Parameter": the parameter of this distribution, having only
the slot name "Parameter of an absolutely continuous distribution"
rObject of class "function": generates random numbers
dObject of class "function": density function
pObject of class "function": cumulative distribution function
qObject 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.
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject of class "DistributionSymmetry";
used internally to avoid unnecessary calculations.
Class "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.
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.
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.
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
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.
## in RStudio or Jupytier IRKernel, use q.l(.)(.) instead of q(.)(.)
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