# 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, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
HellingerDist(e1,e2)
## S3 method for class 'AbscontDistribution,DiscreteDistribution':
HellingerDist(e1,e2)
## S3 method for class 'DiscreteDistribution,AbscontDistribution':
HellingerDist(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
HellingerDist(e1,e2)
##### Arguments
e1
object of class "Distribution"
e2
object of class "Distribution"
...
further arguments to be used in particular methods (not in package distrEx)
##### 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

distance

##### References

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

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 1.9, License: GPL (version 2 or later)

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