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)

Arguments

object of class "Distribution": ideal distribution

object of class "Distribution": contaminating distribution

size

size of contamination (amount of gross errors)

Value

"Distribution".

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".

References

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

Examples

Run this code

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

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