# ContaminationSize

##### Generic Function for the Computation of the Convex Contamination (Pseudo-)Distance of Two Distributions

Generic function for the computation of convex contamination (pseudo-)distance of two probability distributions \(P\) and \(Q\). That is, the minimal size \(\varepsilon\in [0,1]\) is computed such that there exists some probability distribution \(R\) with $$Q = (1-\varepsilon)P + \varepsilon R$$

- Keywords
- distribution

##### Usage

```
ContaminationSize(e1, e2, ...)
# S4 method for AbscontDistribution,AbscontDistribution
ContaminationSize(e1,e2)
# S4 method for DiscreteDistribution,DiscreteDistribution
ContaminationSize(e1,e2)
# S4 method for AcDcLcDistribution,AcDcLcDistribution
ContaminationSize(e1,e2)
```

##### Arguments

- e1
object of class

`"Distribution"`

- e2
object of class

`"Distribution"`

- …
further arguments to be used in particular methods (not in package distrEx)

##### Details

Computes the distance from `e1`

to `e2`

respectively
\(P\) to \(Q\). This is not really a distance as it is not symmetric!

##### Value

A list containing the following components:

object of class `"Distribution"`

; ideal distribution

object of class `"Distribution"`

; 'contaminated' distribution

size of contamination

##### Methods

- e1 = "AbscontDistribution", e2 = "AbscontDistribution":
convex contamination (pseudo-)distance of two absolutely continuous univariate distributions.

- e1 = "DiscreteDistribution", e2 = "DiscreteDistribution":
convex contamination (pseudo-)distance of two discrete univariate distributions.

- e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution":
convex contamination (pseudo-)distance of two discrete univariate distributions.

##### References

Huber, P.J. (1981) *Robust Statistics*. New York: Wiley.

##### See Also

`KolmogorovDist`

, `TotalVarDist`

,
`HellingerDist`

, `Distribution-class`

##### Examples

```
# NOT RUN {
ContaminationSize(Norm(), Norm(mean=0.1))
ContaminationSize(Pois(), Pois(1.5))
# }
```

*Documentation reproduced from package distrEx, version 2.8.0, License: LGPL-3*