distrEx (version 2.0.1)

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, ...)
## S3 method for class 'UnivariateDistribution,UnivariateDistribution':
CvMDist(e1, e2, mu = e2, useApply = FALSE, ...)
## S3 method for class 'numeric,UnivariateDistribution':
CvMDist(e1, e2, mu = e2, ...)

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

concept

distance

References

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

See Also

ContaminationSize, TotalVarDist, HellingerDist, KolmogorovDist, Distribution-class

Examples

Run this code
CvMDist(Norm(), Gumbel())
CvMDist(Norm(), Gumbel(), 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())

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