CvMDist {distrEx} | R Documentation |
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
.
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.
ContaminationSize
, TotalVarDist
,
HellingerDist
, KolmogorovDist
,
Distribution-class
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())