distrEx (version 2.8.0)

ContaminationSize: 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 AbscontDistribution,AbscontDistribution
ContaminationSize(e1,e2)
# S4 method for DiscreteDistribution,DiscreteDistribution
ContaminationSize(e1,e2)
# S4 method for AcDcLcDistribution,AcDcLcDistribution
ContaminationSize(e1,e2)

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

Arguments

e1

object of class "Distribution"

e2

object of class "Distribution"

...

further arguments to be used in particular methods (not in package distrEx)

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

Matthias Kohl ,
Peter Ruckdeschel

Details

Computes the distance from e1 to e2 respectively \(P\) to \(Q\). This is not really a distance as it is not symmetric!

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))