ContaminationSize {distrEx} R Documentation

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

### Description

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

### Usage

ContaminationSize(e1, e2, ...)
## S4 method for signature 'AbscontDistribution,AbscontDistribution'
ContaminationSize(e1,e2)
## S4 method for signature 'DiscreteDistribution,DiscreteDistribution'
ContaminationSize(e1,e2)
## S4 method for signature '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.

### Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### References

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

KolmogorovDist, TotalVarDist, HellingerDist, Distribution-class
ContaminationSize(Norm(), Norm(mean=0.1))