Generic function for the computation of the Cramer - von Mises distance of two distributions
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.
CvMDist(e1, e2, ...) ## S4 method for signature 'UnivariateDistribution,UnivariateDistribution' CvMDist(e1, e2, mu = e1, useApply = FALSE, ..., diagnostic = FALSE) ## S4 method for signature 'numeric,UnivariateDistribution' CvMDist(e1, e2, mu = e1, ..., diagnostic = FALSE)
e1 |
object of class |
e2 |
object of class |
... |
further arguments to be used e.g. by |
useApply |
logical; to be passed to |
mu |
object of class |
diagnostic |
logical; if |
Diagnostics on the involved integrations are available if argument
diagnostic is TRUE. Then there is attribute diagnostic
attached to the return value, which may be inspected
and accessed through showDiagnostic and
getDiagnostic.
Cramer - von Mises distance of e1 and e2
Cramer - von Mises distance of two univariate distributions.
Cramer - von Mises distance between the empirical formed from a data set (e1) and a univariate distribution.
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
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())Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.