distrEx (version 1.9)

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

Description

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 $$d_v(P,Q)=\sup_{B\in{\cal A}}|P(B)-Q(B)|$$

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:
• e1
  object of class "Distribution"; distribution 1
• e2
  object of class "Distribution"; distribution 2
• total.variation.distance
  total 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

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))