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, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
ContaminationSize(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
ContaminationSize(e1,e2)
## S3 method for class 'AcDcLcDistribution,AcDcLcDistribution':
ContaminationSize(e1,e2)

Arguments

object of class "Distribution"

...

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

Value

A list containing the following components:
e1object of class "Distribution"; ideal distribution
e2object of class "Distribution"; 'contaminated' distribution
size.of.contaminationsize of contamination

concept

convex contamination
gross error
distance

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.

Examples

Run this code

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

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