KolmogorovDist {distrEx} | R Documentation |
Generic function for the computation of the Kolmogorov distance d_\kappa
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 Kolmogorov distance is defined as
d_\kappa(P,Q)=\sup\{|P(\{y\in\R^m\,|\,y\le x\})-Q(\{y\in\R^m\,|\,y\le x\})| | x\in\R^m\}
where \le
is coordinatewise on \R^m
.
KolmogorovDist(e1, e2, ...)
## S4 method for signature 'AbscontDistribution,AbscontDistribution'
KolmogorovDist(e1,e2, ...)
## S4 method for signature 'AbscontDistribution,DiscreteDistribution'
KolmogorovDist(e1,e2, ...)
## S4 method for signature 'DiscreteDistribution,AbscontDistribution'
KolmogorovDist(e1,e2, ...)
## S4 method for signature 'DiscreteDistribution,DiscreteDistribution'
KolmogorovDist(e1,e2, ...)
## S4 method for signature 'numeric,UnivariateDistribution'
KolmogorovDist(e1, e2, ...)
## S4 method for signature 'UnivariateDistribution,numeric'
KolmogorovDist(e1, e2, ...)
## S4 method for signature 'AcDcLcDistribution,AcDcLcDistribution'
KolmogorovDist(e1, e2, ...)
e1 |
object of class |
e2 |
object of class |
... |
further arguments to be used in particular methods (not in package distrEx) |
Kolmogorov distance of e1
and e2
Kolmogorov distance of two absolutely continuous univariate distributions which is computed using a union of a (pseudo-)random and a deterministic grid.
Kolmogorov distance of two discrete univariate distributions.
The distance is attained at some point of the union of the supports
of e1
and e2
.
Kolmogorov distance of absolutely continuous and discrete
univariate distributions. It is computed using a union of
a (pseudo-)random and a deterministic grid in combination
with the support of e2
.
Kolmogorov distance of discrete and absolutely continuous
univariate distributions. It is computed using a union of
a (pseudo-)random and a deterministic grid in combination
with the support of e1
.
Kolmogorov distance between (empirical) data and a univariate
distribution. The computation is based on ks.test
.
Kolmogorov distance between (empirical) data and a univariate
distribution. The computation is based on ks.test
.
Kolmogorov distance of mixed discrete and absolutely continuous
univariate distributions. It is computed using a union of
the discrete part, a (pseudo-)random and
a deterministic grid in combination
with the support of e1
.
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
Huber, P.J. (1981) Robust Statistics. New York: Wiley.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
ContaminationSize
, TotalVarDist
,
HellingerDist
, Distribution-class
KolmogorovDist(Norm(), UnivarMixingDistribution(Norm(1,2),Norm(0.5,3),
mixCoeff=c(0.2,0.8)))
KolmogorovDist(Norm(), Td(10))
KolmogorovDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100))
KolmogorovDist(Pois(10), Binom(size = 20))
KolmogorovDist(Norm(), rnorm(100))
KolmogorovDist((rbinom(50, size = 20, prob = 0.5)-10)/sqrt(5), Norm())
KolmogorovDist(rbinom(50, size = 20, prob = 0.5), Binom(size = 20, prob = 0.5))