# 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 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"`

##### See Also

`AbscontDistribution-class`

,
`DiscreteDistribution-class`

,
`RtoDPQ`

##### Examples

```
# NOT RUN {
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 2.7.0, License: LGPL-3*