# ContaminationSize

From distrEx v0.4-2
by Matthias Kohl

##### 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)`

##### Arguments

- e1
- object of class
`"Distribution"`

- e2
- object of class
`"Distribution"`

##### 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:
e1 object of class `"Distribution"`

; ideal distributione2 object of class `"Distribution"`

; 'contaminated' distributionsize.of.contamination size of contamination

##### concept

- convex contamination
- gross error

##### References

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

##### See Also

`KolmogorovDist`

, `TotalVarDist`

,
`HellingerDist`

, `Distribution-class`

##### Examples

```
ContaminationSize(Norm(), Norm(mean=0.1))
ContaminationSize(Pois(), Pois(1.5))
```

*Documentation reproduced from package distrEx, version 0.4-2, License: GPL (version 2 or later)*

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