R: Generic function for the computation of the Cramer - von...

CvMDist {distrEx} | R Documentation

## Generic function for the computation of the Cramer - von Mises distance of two distributions

### Description

Generic function for the computation of the Cramer - von Mises distance d_{mu} of two distributions P and Q where the distributions are defined on a finite-dimensional Euclidean space (R^m, B^m) with B^m the Borel-sigma-algebra on R^m. The Cramer - von Mises distance is defined as

d_{mu}(P,Q)^2=\int (P({y in R^m | y <= x})-Q({y in R^m | y <= x}))^2 mu(dx)

where <= is coordinatewise on R^m.

### Usage

    CvMDist(e1, e2, ...)
    ## S4 method for signature 'UnivariateDistribution,UnivariateDistribution'
    CvMDist(e1, e2, mu = e1, useApply = FALSE, ...)
    ## S4 method for signature 'numeric,UnivariateDistribution'
    CvMDist(e1, e2, mu = e1, ...)

### Arguments

`e1` | object of class `"Distribution"` or class `"numeric"`
`e2` | object of class `"Distribution"`
`...` | further arguments to be used e.g. by `E()`
`useApply` | logical; to be passed to `E()`
`mu` | object of class `"Distribution"`; integration measure; defaulting to `e2`

### Value

Cramer - von Mises distance of `e1` and `e2`

### Methods

e1 = "UnivariateDistribution", e2 = "UnivariateDistribution":

  Cramer - von Mises distance of two univariate distributions.

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

  Cramer - von Mises distance between the empirical formed from a data set (e1) and a univariate distribution.

### Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

### See Also

`ContaminationSize`, `TotalVarDist`, `HellingerDist`, `KolmogorovDist`, `Distribution-class`

### Examples

    CvMDist(Norm(), UnivarMixingDistribution(Norm(1,2),Norm(0.5,3),
                     mixCoeff=c(0.2,0.8)))
    CvMDist(Norm(), UnivarMixingDistribution(Norm(1,2),Norm(0.5,3),
                     mixCoeff=c(0.2,0.8)),mu=Norm())
    CvMDist(Norm(), Td(10))
    CvMDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100))
    CvMDist(Pois(10), Binom(size = 20))
    CvMDist(rnorm(100),Norm())
    CvMDist((rbinom(50, size = 20, prob = 0.5)-10)/sqrt(5), Norm())
    CvMDist(rbinom(50, size = 20, prob = 0.5), Binom(size = 20, prob = 0.5))
    CvMDist(rbinom(50, size = 20, prob = 0.5), Binom(size = 20, prob = 0.5), mu = Pois())

[Package distrEx version 2.7.0 Index]