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

The Hellinger distance of two probability distributions is computed.

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 0-4.1 Index]