# AbscontDistribution

From distr v2.6
by Peter Ruckdeschel

##### 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 | r | d | p |

`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

`"AbscontDistribution"`

##### 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 2.6, License: LGPL-3*

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