distrEx: ContaminationSize – R documentation

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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 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.

Examples

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

distrEx

Extensions of Package 'distr'

v2.8.0

LGPL-3

Authors

Matthias Kohl [cre, cph], Peter Ruckdeschel [aut, cph]

Initial release

2019-03-29