AbscontDistribution {distr}

Generating function "AbscontDistribution"

Description

Generates an object of class "AbscontDistribution"

Usage

AbscontDistribution(r = NULL, d = NULL, p = NULL, q = NULL,
                   gaps = NULL, param = NULL, img = new("Reals"),
                   .withSim = FALSE, .withArith = FALSE,
                    .lowerExact = FALSE, .logExact = FALSE,
                   withgaps = getdistrOption("withgaps"),
                   low1 = NULL, up1 = NULL, low = -Inf, up =Inf,
                   withStand = FALSE,
                   ngrid = getdistrOption("DefaultNrGridPoints"),
                   ep = getdistrOption("TruncQuantile"),
                   e = getdistrOption("RtoDPQ.e"),
                   Symmetry = NoSymmetry())

Arguments

r

slot r to be filled

d

slot d to be filled

p

slot p to be filled

q

slot q to be filled

gaps

slot gaps (of class "matrix" with two columns) to be filled (i.e. t(gaps) must be ordered if read as vector)

param

parameter (of class "OptionalParameter")

img

image range of the distribution (of class "rSpace")

low1

lower bound (to be the lower TruncQuantile-quantile of the distribution)

up1

upper bound (to be the upper TruncQuantile-quantile of the distribution)

low

lower bound (to be the 100-percent-quantile of the distribution)

up

upper bound (to be the 100-percent-quantile of the distribution)

withStand

logical: shall we standardize argument function d to integrate to 1 — default is no resp. FALSE

ngrid

number of gridpoints

ep

tolerance epsilon

e

exponent to base 10 to be used for simulations

withgaps

logical; shall gaps be reconstructed empirically?

.withArith

normally not set by the user, but if determining the entries supp, prob distributional arithmetics was involved, you may set this to TRUE.

.withSim

normally not set by the user, but if determining the entries supp, prob simulations were involved, you may set this to TRUE.

.lowerExact

normally not set by the user: whether the lower.tail=FALSE part is calculated exactly, avoing a “1-.”.

.logExact

normally not set by the user: whether in determining slots d,p,q, we make particular use of a logarithmic representation to enhance accuracy.

Symmetry

you may help R in calculations if you tell it whether the distribution is non-symmetric (default) or symmetric with respect to a center; in this case use Symmetry=SphericalSymmetry(center).

Details

Typical usages are

  AbscontDistribution(r)
  AbscontDistribution(r = NULL, d)
  AbscontDistribution(r = NULL, d = NULL, p)
  AbscontDistribution(r = NULL, d = NULL, p = NULL, d)
  AbscontDistribution(r, d, p, q)
  

Minimally, only one of the slots r, d, p or q needs to be given as argument. The other non-given slots are then reconstructed according to the following scheme:

r	d	p	q	proceding
-	-	-	-	excluded
-	+	-	-	p by .D2P, q by .P2Q, r by q(runif(n))
-	-	+	-	d by .P2D, q by .P2Q, r by q(runif(n))
-	+	+	-	q by .P2Q, r by q(runif(n))
-	-	-	+	p by .Q2P, d by .P2D, r by q(runif(n))
-	+	-	+	p by .Q2P, r by q(runif(n))
-	-	+	+	d by .P2D, r by q(runif(n))
-	+	+	+	r by q(runif(n))
+	-	-	-	call to RtoDPQ
+	+	-	-	p by .D2P, q by .P2Q
+	-	+	-	d by .P2D, q by .P2Q
+	+	+	-	q by .P2Q
+	-	-	+	p by .Q2P, d by .P2D
+	+	-	+	p by .Q2P
+	-	+	+	d by .P2D
+	+	+	+	nothing

For this purpose, one may alternatively give arguments low1 and up1 (NULL each by default, and determined through slot q, resp. p, resp. d, resp. r in this order according to availability), for the (finite) range of values in the support of this distribution, as well as the possibly infinite theoretical range given by arguments low and up with default values -Inf, Inf, respectively. Of course all other slots may be specified as arguments.

Value

Object of class "AbscontDistribution"

Author(s)

Peter Ruckdeschel [e-mail]

See Also

AbscontDistribution-class, DiscreteDistribution-class, RtoDPQ

Examples

plot(Norm())
plot(AbscontDistribution(r = rnorm))
plot(AbscontDistribution(d = dnorm))
plot(AbscontDistribution(p = pnorm))
plot(AbscontDistribution(q = qnorm))
plot(Ac <- AbscontDistribution(d = function(x, log = FALSE){
                                   d <- exp(-abs(x^3))
                                   ## unstandardized!!
                                   if(log) d <- log(d)
                                   return(d)}, 
                         withStand = TRUE))