KolmogorovDist {distrEx} | R Documentation |
Generic function for the computation of the Kolmogorov distance of two distributions
Description
Generic function for the computation of the Kolmogorov distance
of two distributions
and
where the distributions are defined
on a finite-dimensional Euclidean space
with
the Borel-
-algebra on
.
The Kolmogorov distance is defined as
where is coordinatewise on
.
Usage
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, ...)
Arguments
e1 |
object of class |
e2 |
object of class |
... |
further arguments to be used in particular methods (not in package distrEx) |
Value
Kolmogorov distance of e1
and e2
Methods
- e1 = "AbscontDistribution", e2 = "AbscontDistribution":
-
Kolmogorov distance of two absolutely continuous univariate distributions which is computed using a union of a (pseudo-)random and a deterministic grid.
- e1 = "DiscreteDistribution", e2 = "DiscreteDistribution":
-
Kolmogorov distance of two discrete univariate distributions. The distance is attained at some point of the union of the supports of
e1
ande2
. - e1 = "AbscontDistribution", e2 = "DiscreteDistribution":
-
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
. - e1 = "DiscreteDistribution", e2 = "AbscontDistribution":
-
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
. - e1 = "numeric", e2 = "UnivariateDistribution":
-
Kolmogorov distance between (empirical) data and a univariate distribution. The computation is based on
ks.test
. - e1 = "UnivariateDistribution", e2 = "numeric":
-
Kolmogorov distance between (empirical) data and a univariate distribution. The computation is based on
ks.test
. - e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution":
-
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
.
Author(s)
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
References
Huber, P.J. (1981) Robust Statistics. New York: Wiley.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
See Also
ContaminationSize
, TotalVarDist
,
HellingerDist
, Distribution-class
Examples
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))