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)

Arguments

e1 object of class "Distribution"
e2 object of class "Distribution"

Value

The total variation distance of two probability distributions is computed.

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 0-4.1 Index]