distrEx (version 2.9.5)

ConvexContamination: Generic Function for Generating Convex Contaminations

Description

Generic function for generating convex contaminations. This is also known as gross error model. Given two distributions \(P\) (ideal distribution), \(R\) (contaminating distribution) and the size \(\varepsilon\in [0,1]\) the convex contaminated distribution $$Q = (1-\varepsilon)P + \varepsilon R$$ is generated.

Usage

ConvexContamination(e1, e2, size)

Value

Object of class "Distribution".

Arguments

e1

object of class "Distribution": ideal distribution

e2

object of class "Distribution": contaminating distribution

size

size of contamination (amount of gross errors)

Methods

e1 = "UnivariateDistribution", e2 = "UnivariateDistribution", size = "numeric":

convex combination of two univariate distributions

e1 = "AbscontDistribution", e2 = "AbscontDistribution", size = "numeric":

convex combination of two absolutely continuous univariate distributions

e1 = "DiscreteDistribution", e2 = "DiscreteDistribution", size = "numeric":

convex combination of two discrete univariate distributions

e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution", size = "numeric":

convex combination of two univariate distributions which may be coerced to "UnivarLebDecDistribution".

Author

Matthias Kohl

References

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

See Also

ContaminationSize, Distribution-class

Examples

# Convex combination of two normal distributions
C1 <- ConvexContamination(e1 = Norm(), e2 = Norm(mean = 5), size = 0.1)
plot(C1)