# AbscontDistribution-class

##### Class "AbscontDistribution"

The `AbscontDistribution`

-class is the mother-class of the classes `Beta`

, `Cauchy`

,
`Chisq`

, `Exp`

, `F`

, `Gammad`

, `Lnorm`

, `Logis`

, `Norm`

, `T`

, `Unif`

and
`Weibull`

. Further absolutely continuous distributions can be defined either by declaration of
own random number generator, density, cumulative distribution and quantile functions, or as result of a
convolution of two absolutely continuous distributions or by application of a mathematical operator to an absolutely
continuous distribution.

- Keywords
- distribution

##### Objects from the Class

Objects can be created by calls of the form `new("AbscontDistribution", r, d, p, q)`

.
More comfortably, you may use the generating function `AbscontDistribution`

.
The result of these calls is an absolutely continuous distribution.

##### Extends

Class `"UnivariateDistribution"`

, directly.
Class `"Distribution"`

, by class `"UnivariateDistribution"`

.

##### Internal subclass "AffLinAbscontDistribution"

To enhance accuracy of several functionals on distributions,
mainly from package `"AffLinAbscontDistribution"`

which has extra slots
`a`

, `b`

(both of class `"numeric"`

), and `X0`

(of class `"AbscontDistribution"`

), to capture the fact
that the object has the same distribution as `a * X0 + b`

. This is
the class of the return value of methods

- -

`signature(e1 = "AbscontDistribution")`

}
`signature(e1 = "AbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "AbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "AbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "AbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "numeric", e2 = "AbscontDistribution")`

}
`signature(e1 = "numeric", e2 = "AbscontDistribution")`

}
`signature(e1 = "numeric", e2 = "AbscontDistribution")`

}
`signature(e1 = "AffLinAbscontDistribution")`

}
`signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "AffLinAbscontDistribution", e2 = "numeric")`

}
`signature(e1 = "numeric", e2 = "AffLinAbscontDistribution")`

}
`signature(e1 = "numeric", e2 = "AffLinAbscontDistribution")`

}
`signature(e1 = "numeric", e2 = "AffLinAbscontDistribution")`

}
##### code

`"AffLinDistribution"`

##### Internal virtual superclass "AcDcLcDistribution"

As many operations should be valid no matter whether the operands
are of class `"AbscontDistribution"`

,
`"DiscreteDistribution"`

, or `"UnivarLebDecDistribution"`

,
there is a class union of these classes called `"AcDcLcDistribution"`

;
in partiucalar methods for `"*"`

, `"/"`

,
`"^"`

(see operators-methods) and methods
`Minimum`

, `Maximum`

, `Truncate`

, and
`Huberize`

, and `convpow`

are defined for this
class union.

##### concept

- absolutely continuous distribution
- S4 distribution class

##### See Also

`AbscontDistribution`

`Parameter-class`

`UnivariateDistribution-class`

`Beta-class`

`Cauchy-class`

`Chisq-class`

`Exp-class`

`Fd-class`

`Gammad-class`

`Lnorm-class`

`Logis-class`

`Norm-class`

`Td-class`

`Unif-class`

`Weibull-class`

`DiscreteDistribution-class`

`Reals-class`

`RtoDPQ`

##### Examples

```
N <- Norm() # N is a normal distribution with mean=0 and sd=1.
E <- Exp() # E is an exponential distribution with rate=1.
A1 <- E+1 # a new absolutely continuous distributions with exact slots d, p, q
A2 <- A1*3 # a new absolutely continuous distributions with exact slots d, p, q
A3 <- N*0.9 + E*0.1 # a new absolutely continuous distribution with approximated slots d, p, q
r(A3)(1) # one random number generated from this distribution, e.g. -0.7150937
d(A3)(0) # The (approximated) density for x=0 is 0.4379882.
p(A3)(0) # The (approximated) probability that x <= 0 is 0.4562021.
q(A3)(.1) # The (approximated) 10 percent quantile is 0.1.
```

*Documentation reproduced from package distr, version 2.0.6, License: LGPL-3*