HellingerDist {distrEx}R Documentation

Generic function for the computation of the Hellinger distance of two distributions

Description

Generic function for the computation of the Hellinger distance d_h of two distributions P and Q which may be defined for an arbitrary sample space (Omega, A). The Hellinger distance is defined as

0.5 int |sqrt{dP}-sqrt{dQ}|^2

where sqrt{dP}, respectively sqrt{dQ} denotes the square root of the densities.

Usage

HellingerDist(e1, e2)

Arguments

e1 object of class "Distribution"
e2 object of class "Distribution"

Value

A list containing the following components:

e1 object of class "Distribution"; distribution 1
e2 object of class "Distribution"; distribution 2
Hellinger.distance Hellinger distance of e1 and e2

Methods

e1 = "AbscontDistribution", e2 = "AbscontDistribution":
Hellinger distance of two absolutely continuous univariate distributions which is computed using distrExintegrate.
e1 = "AbscontDistribution", e2 = "DiscreteDistribution":
Hellinger distance of absolutely continuous and discrete univariate distributions (are mutually singular; i.e., have distance =1).
e1 = "DiscreteDistribution", e2 = "DiscreteDistribution":
Hellinger distance of two discrete univariate distributions which is computed using support and sum.
e1 = "DiscreteDistribution", e2 = "AbscontDistribution":

Hellinger distance of discrete and absolutely continuous univariate distributions (are mutually singular; i.e., have distance =1).

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

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

See Also

distrExIntegrate, ContaminationSize, TotalVarDist, KolmogorovDist, Distribution-class

Examples

HellingerDist(Norm(), Gumbel())
HellingerDist(Norm(), Td(10))
HellingerDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100)) # mutually singular
HellingerDist(Pois(10), Binom(size = 20)) 

[Package distrEx version 1.8 Index]