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 dκd_\kappa of two distributions PP and QQ where the distributions are defined on a finite-dimensional Euclidean space (Rm,Bm)(\R^m,{\cal B}^m) with Bm {\cal B}^m the Borel-σ\sigma-algebra on RmR^m. The Kolmogorov distance is defined as

dκ(P,Q)=sup{P({yRmyx})Q({yRmyx})xRm}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 Rm\R^m.

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 "Distribution" or class "numeric"

e2

object of class "Distribution" or class "numeric"

...

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 and e2.

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))

[Package distrEx version 2.9.2 Index]