# 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, ...)
# 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:

e1

object of class "Distribution"; ideal distribution

e2

object of class "Distribution"; 'contaminated' distribution

size.of.contamination

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.

KolmogorovDist, TotalVarDist, HellingerDist, Distribution-class

##### Aliases
• ContaminationSize
• ContaminationSize-methods
• ContaminationSize,AbscontDistribution,AbscontDistribution-method
• ContaminationSize,DiscreteDistribution,DiscreteDistribution-method
• ContaminationSize,LatticeDistribution,DiscreteDistribution-method
• ContaminationSize,DiscreteDistribution,LatticeDistribution-method
• ContaminationSize,LatticeDistribution,LatticeDistribution-method
• ContaminationSize,AcDcLcDistribution,AcDcLcDistribution-method
##### 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

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