ContaminationSize: Generic Function for the Computation of the Convex... In distrEx: Extensions of Package 'distr'

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

 ```1 2 3 4 5 6 7``` ```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 [email protected],
Peter Ruckdeschel [email protected]

References

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

See Also

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

Examples

 ```1 2``` ```ContaminationSize(Norm(), Norm(mean=0.1)) ContaminationSize(Pois(), Pois(1.5)) ```

distrEx documentation built on May 30, 2017, 3:09 a.m.