R: Generic Function for the Computation of the Convex...

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 0 <= epsilon <= 1 is computed such that there exists some probability distribution R with

Q = (1 - epsilon)P + epsilon 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.

### See Also

`KolmogorovDist`, `TotalVarDist`, `HellingerDist`, `Distribution-class`

### Examples

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

[Package distrEx version 2.7.0 Index]