1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
|
\name{AbscontDistribution}
\alias{AbscontDistribution}
\title{Generating function "AbscontDistribution"}
\description{Generates an object of class \code{"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{
\item{r}{slot \code{r} to be filled}
\item{d}{slot \code{d} to be filled}
\item{p}{slot \code{p} to be filled}
\item{q}{slot \code{q} to be filled}
\item{gaps}{slot gaps (of class \code{"matrix"} with two columns) to be filled
(i.e. \code{t(gaps)} must be ordered if read as vector)}
\item{param}{parameter (of class \code{"OptionalParameter"})}
\item{img}{image range of the distribution (of class \code{"rSpace"})}
\item{low1}{lower bound (to be the lower TruncQuantile-quantile of the distribution)}
\item{up1}{upper bound (to be the upper TruncQuantile-quantile of the distribution)}
\item{low}{lower bound (to be the 100-percent-quantile of the distribution)}
\item{up}{upper bound (to be the 100-percent-quantile of the distribution)}
\item{withStand}{logical: shall we standardize argument function \code{d}
to integrate to 1 --- default is no resp. \code{FALSE}}
\item{ngrid}{number of gridpoints}
\item{ep}{tolerance epsilon}
\item{e}{exponent to base 10 to be used for simulations}
\item{withgaps}{logical; shall gaps be reconstructed empirically?}
\item{.withArith}{normally not set by the user, but if determining the entries \code{supp}, \code{prob}
distributional arithmetics was involved, you may set this to \code{TRUE}.}
\item{.withSim}{normally not set by the user, but if determining the entries \code{supp}, \code{prob}
simulations were involved, you may set this to \code{TRUE}.}
\item{.lowerExact}{normally not set by the user: whether the \code{lower.tail=FALSE}
part is calculated exactly, avoing a ``\code{1-.}''.}
\item{.logExact}{normally not set by the user: whether in determining slots \code{d,p,q},
we make particular use of a logarithmic representation to enhance accuracy.}
\item{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 \code{Symmetry=SphericalSymmetry(center)}.}
}
\details{
Typical usages are
\preformatted{
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 \code{r}, \code{d}, \code{p} or \code{q} needs to be given as argument.
The other non-given slots are then reconstructed according to the following scheme:
\tabular{ccccl}{
r\tab d\tab p\tab q\tab proceding\cr
-\tab -\tab -\tab -\tab excluded\cr
-\tab +\tab -\tab -\tab p by \code{.D2P}, q by \code{.P2Q}, r by \code{q(runif(n))}\cr
-\tab -\tab +\tab -\tab d by \code{.P2D}, q by \code{.P2Q}, r by \code{q(runif(n))}\cr
-\tab +\tab +\tab -\tab q by \code{.P2Q}, r by \code{q(runif(n))}\cr
-\tab -\tab -\tab +\tab p by \code{.Q2P}, d by \code{.P2D}, r by \code{q(runif(n))}\cr
-\tab +\tab -\tab +\tab p by \code{.Q2P}, r by \code{q(runif(n))}\cr
-\tab -\tab +\tab +\tab d by \code{.P2D}, r by \code{q(runif(n))}\cr
-\tab +\tab +\tab +\tab r by \code{q(runif(n))}\cr
+\tab -\tab -\tab -\tab call to \code{\link{RtoDPQ}}\cr
+\tab +\tab -\tab -\tab p by \code{.D2P}, q by \code{.P2Q}\cr
+\tab -\tab +\tab -\tab d by \code{.P2D}, q by \code{.P2Q}\cr
+\tab +\tab +\tab -\tab q by \code{.P2Q}\cr
+\tab -\tab -\tab +\tab p by \code{.Q2P}, d by \code{.P2D}\cr
+\tab +\tab -\tab +\tab p by \code{.Q2P}\cr
+\tab -\tab +\tab +\tab d by \code{.P2D}\cr
+\tab +\tab +\tab +\tab nothing\cr}
For this purpose, one may alternatively give arguments \code{low1} and \code{up1} (\code{NULL} each by default,
and determined through slot \code{q}, resp. \code{p}, resp. \code{d}, resp. \code{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 \code{low} and \code{up} with default values \code{-Inf}, \code{Inf}, respectively.
Of course all other slots may be specified as arguments.}
\value{Object of class \code{"AbscontDistribution"}}
\author{
Peter Ruckdeschel \email{peter.ruckdeschel@uni-oldenburg.de}
}
\seealso{
\code{\link{AbscontDistribution-class}},
\code{\link{DiscreteDistribution-class}},
\code{\link{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))
}
\keyword{distribution}
\concept{absolutely continuous distribution}
\concept{generating function}
|
