# ConvexContamination

##### 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.

##### See Also

##### 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*