# AbscontDistribution

##### Generating function "AbscontDistribution"

Generates an object of class `"AbscontDistribution"`

- Keywords
- distribution

##### 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 Rin 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:
`.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"`

##### concept

- absolutely continuous distribution
- generating function

##### 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))
```

*Documentation reproduced from package distr, version 2.3.1, License: LGPL-3*