distrEx (version 2.6.1)

CvMDist: 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 \((\R^m,{\cal B}^m)\) with \( {\cal B}^m \) the Borel-\(\sigma\)-algebra on \(R^m\). The Cramer - von Mises distance is defined as $$d_\mu(P,Q)^2=\int\,(P(\{y\in\R^m\,|\,y\le x\})-Q(\{y\in\R^m\,|\,y\le x\}))^2\,\mu(dx)$$ where \(\le\) is coordinatewise on \(\R^m\).

Usage

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

References

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

See Also

ContaminationSize, TotalVarDist, HellingerDist, KolmogorovDist, Distribution-class

Examples

# NOT RUN {
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())
# }