HellingerDist

0th

Percentile

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

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.

Keywords
distribution
Usage
HellingerDist(e1, e2)
Arguments
e1
object of class "Distribution"
e2
object of class "Distribution"
Value

  • A list containing the following components:
  • e1object of class "Distribution"; distribution 1
  • e2object of class "Distribution"; distribution 2
  • Hellinger.distanceHellinger 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

Aliases
  • HellingerDist
  • HellingerDist-methods
  • HellingerDist,AbscontDistribution,AbscontDistribution-method
  • HellingerDist,AbscontDistribution,DiscreteDistribution-method
  • HellingerDist,DiscreteDistribution,DiscreteDistribution-method
  • HellingerDist,DiscreteDistribution,AbscontDistribution-method
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))
Documentation reproduced from package distrEx, version 0.4-2, License: GPL (version 2 or later)

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