ContaminationSize

0th

Percentile

Generic Function for the Computation of the Convex Contamination (Pseudo-)Distance of Two Distributions

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 $$Q = (1-\varepsilon)P + \varepsilon R$$

Keywords
distribution
Usage
ContaminationSize(e1, e2, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
ContaminationSize(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
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:
  • e1object of class "Distribution"; ideal distribution
  • e2object of class "Distribution"; 'contaminated' distribution
  • size.of.contaminationsize of contamination

concept

  • convex contamination
  • gross error
  • distance

References

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

See Also

KolmogorovDist, TotalVarDist, HellingerDist, Distribution-class

Aliases
  • ContaminationSize
  • ContaminationSize-methods
  • ContaminationSize,AbscontDistribution,AbscontDistribution-method
  • ContaminationSize,DiscreteDistribution,DiscreteDistribution-method
Examples
ContaminationSize(Norm(), Norm(mean=0.1))
ContaminationSize(Pois(), Pois(1.5))
Documentation reproduced from package distrEx, version 1.9, License: GPL (version 2 or later)

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