KolmogorovDist: Generic function for the computation of the Kolmogorov distance of two distributions

Description

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_{κ} (P, Q) = sup | P (y \in \R^{m} | y \leq x) - Q (y \in \R^{m} | y \leq x) | | x \in \R^{m}

where $\le$ is coordinatewise on $\R^m$.

Usage

KolmogorovDist(e1, e2, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'AbscontDistribution,DiscreteDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'DiscreteDistribution,AbscontDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'numeric,UnivariateDistribution':
KolmogorovDist(e1, e2)
## S3 method for class 'UnivariateDistribution,numeric':
KolmogorovDist(e1, e2)
## S3 method for class 'AcDcLcDistribution,AcDcLcDistribution':
KolmogorovDist(e1, e2)

Arguments

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

concept

distance

References

Huber, P.J. (1981) Robust Statistics. New York: Wiley. Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Examples

Run this code

KolmogorovDist(Norm(), Gumbel())
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))

Run the code above in your browser using DataLab

Get 50% off unlimited learning