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)
Arguments
e1 |
object of class "Distribution" |
e2 |
object of class "Distribution" |
Value
The Kolmogorov distance of two probability distributions
is computed.
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
.
Author(s)
Matthias Kohl Matthias.Kohl@stamats.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(), Gumbel())
KolmogorovDist(Norm(), Td(10))
KolmogorovDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100))
KolmogorovDist(Pois(10), Binom(size = 20))
[Package
distrEx version 0-4.1
Index]