# ContaminationSize

0th

Percentile

##### 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, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
ContaminationSize(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
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:
• e1object of class "Distribution"; ideal distribution
• e2object of class "Distribution"; 'contaminated' distribution
• size.of.contaminationsize of contamination

##### concept

• convex contamination
• gross error
• distance

##### References

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

KolmogorovDist, TotalVarDist, HellingerDist, Distribution-class

##### Aliases
• ContaminationSize
• ContaminationSize-methods
• ContaminationSize,AbscontDistribution,AbscontDistribution-method
• ContaminationSize,DiscreteDistribution,DiscreteDistribution-method
##### Examples
ContaminationSize(Norm(), Norm(mean=0.1))
ContaminationSize(Pois(), Pois(1.5))
Documentation reproduced from package distrEx, version 1.9, License: GPL (version 2 or later)

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