# KolmogorovDist

0th

Percentile

##### Generic function for the computation of the Kolmogorov distance of two distributions

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 $$\R^m$$.

Keywords
distribution
##### Usage
KolmogorovDist(e1, e2, ...)
# S4 method for AbscontDistribution,AbscontDistribution
KolmogorovDist(e1,e2)
# S4 method for AbscontDistribution,DiscreteDistribution
KolmogorovDist(e1,e2)
# S4 method for DiscreteDistribution,AbscontDistribution
KolmogorovDist(e1,e2)
# S4 method for DiscreteDistribution,DiscreteDistribution
KolmogorovDist(e1,e2)
# S4 method for numeric,UnivariateDistribution
KolmogorovDist(e1, e2)
# S4 method for UnivariateDistribution,numeric
KolmogorovDist(e1, e2)
# S4 method for 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.

##### References

Huber, P.J. (1981) Robust Statistics. New York: Wiley.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

ContaminationSize, TotalVarDist, HellingerDist, Distribution-class

##### Aliases
• KolmogorovDist
• KolmogorovDist-methods
• KolmogorovDist,AbscontDistribution,AbscontDistribution-method
• KolmogorovDist,AbscontDistribution,DiscreteDistribution-method
• KolmogorovDist,DiscreteDistribution,DiscreteDistribution-method
• KolmogorovDist,DiscreteDistribution,AbscontDistribution-method
• KolmogorovDist,LatticeDistribution,DiscreteDistribution-method
• KolmogorovDist,DiscreteDistribution,LatticeDistribution-method
• KolmogorovDist,LatticeDistribution,LatticeDistribution-method
• KolmogorovDist,numeric,UnivariateDistribution-method
• KolmogorovDist,UnivariateDistribution,numeric-method
• KolmogorovDist,AcDcLcDistribution,AcDcLcDistribution-method
##### Examples
# NOT RUN {
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))
# }

Documentation reproduced from package distrEx, version 2.8.0, License: LGPL-3

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