R: Generic function for the computation of the Kolmogorov...

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 d_k of two distributions P and Q where the distributions are defined on a finite-dimensional Euclidean space (R^m, B^m) with B^m the Borel-sigma-algebra on R^m. The Kolmogorov distance is defined as

d_k(P,Q)=\sup{|P({y in R^m | y <= x})-Q({y in R^m | y <= x})| | x in R^m}

where ≤ is coordinatewise on 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 2.8.0 Index]