# CvMDist: Generic function for the computation of the Cramer - von... In distrEx: Extensions of Package 'distr'

## 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

 1 2 3 4 5 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 [email protected],
Peter Ruckdeschel [email protected]

## References

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

ContaminationSize, TotalVarDist, HellingerDist, KolmogorovDist, Distribution-class
  1 2 3 4 5 6 7 8 9 10 11 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())