TotalVarDist

0th

Percentile

Generic function for the computation of the total variation distance of two distributions

Generic function for the computation of the total variation distance $d_v$ of two distributions $P$ and $Q$ where the distributions may be defined for an arbitrary sample space $(\Omega,{\cal A})$. The total variation distance is defined as $$d_v(P,Q)=\sup_{B\in{\cal A}}|P(B)-Q(B)|$$

Keywords
distribution
Usage
TotalVarDist(e1, e2, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
TotalVarDist(e1,e2)
## S3 method for class 'AbscontDistribution,DiscreteDistribution':
TotalVarDist(e1,e2)
## S3 method for class 'DiscreteDistribution,AbscontDistribution':
TotalVarDist(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
TotalVarDist(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
  • total.variation.distancetotal variation distance of e1 and e2

concept

distance

References

Huber, P.J. (1981) Robust Statistics. New York: Wiley.

See Also

TotalVarDist-methods, ContaminationSize, KolmogorovDist, HellingerDist, Distribution-class

Aliases
  • TotalVarDist
  • TotalVarDist-methods
  • TotalVarDist,AbscontDistribution,AbscontDistribution-method
  • TotalVarDist,AbscontDistribution,DiscreteDistribution-method
  • TotalVarDist,DiscreteDistribution,DiscreteDistribution-method
  • TotalVarDist,DiscreteDistribution,AbscontDistribution-method
Examples
TotalVarDist(Norm(), Gumbel())
TotalVarDist(Norm(), Td(10))
TotalVarDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100)) # mutually singular
TotalVarDist(Pois(10), Binom(size = 20))
Documentation reproduced from package distrEx, version 1.9, License: GPL (version 2 or later)

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