distrEx (version 0.4-2)

HellingerDist: 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 $(\Omega,{\cal A})$. The Hellinger distance is defined as $$d_h(P,Q)=\frac{1}{2}\int|\sqrt{dP}\,-\sqrt{dQ}\,|^2$$ 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

concept

distance

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))