# ConvexContamination

0th

Percentile

##### Generic Function for Generating Convex Contaminations

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.

Keywords
methods, distribution
##### Usage
ConvexContamination(e1, e2, size)
##### Arguments
e1

object of class "Distribution": ideal distribution

e2

object of class "Distribution": contaminating distribution

size

size of contamination (amount of gross errors)

##### Value

Object of class "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.

ContaminationSize, Distribution-class

##### Aliases
• ConvexContamination
• ConvexContamination-methods
• ConvexContamination,UnivariateDistribution,UnivariateDistribution,numeric-method
• ConvexContamination,AbscontDistribution,AbscontDistribution,numeric-method
• ConvexContamination,AbscontDistribution,UnivariateDistribution,numeric-method
• ConvexContamination,DiscreteDistribution,DiscreteDistribution,numeric-method
• ConvexContamination,LatticeDistribution,DiscreteDistribution,numeric-method
• ConvexContamination,DiscreteDistribution,LatticeDistribution,numeric-method
• ConvexContamination,LatticeDistribution,LatticeDistribution,numeric-method
• ConvexContamination,AcDcLcDistribution,AcDcLcDistribution,numeric-method
##### Examples
# NOT RUN {
# Convex combination of two normal distributions
C1 <- ConvexContamination(e1 = Norm(), e2 = Norm(mean = 5), size = 0.1)
plot(C1)
# }

Documentation reproduced from package distrEx, version 2.8.0, License: LGPL-3

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