distrEx (version 2.6.1)

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)

Arguments

e1

object of class "Distribution"

e2

object of class "Distribution"

…

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

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.

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

# NOT RUN {
ContaminationSize(Norm(), Norm(mean=0.1))
ContaminationSize(Pois(), Pois(1.5))
# }

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