TotalVarDist {distrEx}R Documentation

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, A). The total variation distance is defined as

d_v(P,Q)=sup{|P(B)-Q(B)| | B in A}

Usage

TotalVarDist(e1, e2, ...)
## S4 method for signature 'AbscontDistribution,
##   AbscontDistribution':
TotalVarDist(e1,e2)
## S4 method for signature 'AbscontDistribution,
##   DiscreteDistribution':
TotalVarDist(e1,e2)
## S4 method for signature 'DiscreteDistribution,
##   AbscontDistribution':
TotalVarDist(e1,e2)
## S4 method for signature '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

Methods

e1 = "AbscontDistribution", e2 = "AbscontDistribution":
total variation distance of two absolutely continuous univariate distributions which is computed using distrExIntegrate.
e1 = "AbscontDistribution", e2 = "DiscreteDistribution":
total variation distance of absolutely continuous and discrete univariate distributions (are mutually singular; i.e., have distance =1).
e1 = "DiscreteDistribution", e2 = "DiscreteDistribution":
total variation distance of two discrete univariate distributions which is computed using support and sum.
e1 = "DiscreteDistribution", e2 = "AbscontDistribution":
total variation distance of discrete and absolutely continuous univariate distributions (are mutually singular; i.e., have distance =1).

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

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)) 

[Package distrEx version 1.9 Index]