# UnivarLebDecDistribution-class

##### Class "UnivarLebDecDistribution"

`UnivarLebDecDistribution`

-class is a class to formalize
a Lebesgue decomposed distribution with a discrete and an
absolutely continuous part; it is a subclass to
class `UnivarMixingDistribution`

.

- Keywords
- distribution

##### Objects from the Class

Objects can be created by calls of the form
`new("UnivarLebDecDistribution", ...)`

.
More frequently they are created via the generating function
`UnivarLebDecDistribution`

.

##### Extends

Class `"UnivarMixingDistribution"`

, directly;
class `"UnivariateDistribution"`

by class `"UnivarMixingDistribution"`

class `"Distribution"`

by class `"UnivariateDistribution"`

.

##### Internal subclass "AffLinUnivarLebDecDistribution"

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

which has extra slots
`a`

, `b`

(both of class `"numeric"`

), and `X0`

(of class `"UnivarLebDecDistribution"`

), 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 = "UnivarLebDecDistribution")`

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

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

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

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

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

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

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

}
`signature(e1 = "AffLinUnivarLebDecDistribution")`

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

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

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

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

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

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

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

}
##### 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 particular methods for `"*"`

, `"/"`

,
`"^"`

(see operators-methods) and methods
`Minimum`

, `Maximum`

, `Truncate`

, and
`Huberize`

, and `convpow`

are defined for this
class union.

##### concept

- Lebesgue decomposed distribution
- absolutely continuous distribution
- discrete distribution
- S4 distribution class

##### See Also

`Parameter-class`

`UnivarMixingDistribution-class`

`DiscreteDistribution-class`

`AbscontDistribution-class`

`simplifyD`

`flat.LCD`

##### Examples

```
wg <- flat.mix(UnivarMixingDistribution(Unif(0,1),Unif(4,5),
withSimplify=FALSE))
myLC <- UnivarLebDecDistribution(discretePart=Binom(3,.3), acPart = wg,
discreteWeight=.2)
myLC
p(myLC)(0.3)
r(myLC)(30)
q(myLC)(0.9)
acPart(myLC)
plot(myLC)
d.discrete(myLC)(2)
p.ac(myLC)(0)
acWeight(myLC)
plot(acPart(myLC))
plot(discretePart(myLC))
gaps(myLC)
support(myLC)
plot(as(Norm(),"UnivarLebDecDistribution"))
```

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