TVD: Total variation distance

In CarolinaEuan/HMClust: HMClust

Total variation distance

Description

Computes the total variation distance between f1 and f2 with respect to the values w using the trapezoidal rule.

Usage

TVD(w, f1, f2)

Arguments

w	Sorted vector of w values.
f1,f2	Numeric vectors with the values of f1(w) and f2(w) which are going to be compare. f1,f2 and w must have the same length. f1 and f2 must be normalized functions.

Details

The TVD between two probability densities, f1 and f2, is defined as

d_TV(f1,f2) = 1 - integral( min(f1(w),f2(w)) dw).

Value

A numeric value between [0,1].

Author(s)

Carolina Euan.

Examples

##TVD between two normal densities 
w<-seq(0,5,length=1000)
f1<-dnorm(w,2,.5)
f2<-dnorm(w,2.5,.5)
diss<-TVD(w,f1,f2)
plot(w,f1,type="l",lwd=2,col=2,main=paste("TVD =",round(diss,3)),
      xlab="x",ylab="")
lines(w,f2,col=3,lwd=2)

##TVD between the normalized spectra of two AR2 processes
X1<-Sim.Ar(1000,12,1.01,100)
X2<-Sim.Ar(1000,15,1.01,100)
fest1<-spec.parzen(X1,a=300,dt=1/100)
fest2<-spec.parzen(X2,a=300,dt=1/100)
diss<-TVD(fest1[,1],fest1[,2]/var(X1),fest2[,2]/var(X2))
plot(fest1[,1],fest1[,2]/var(X1),type="l",lwd=2,col=2,main=paste("TVD =",round(diss,3)),xlab="w (Hz)",ylab="",ylim=c(0,max(fest1[,2]/var(X1),fest2[,2]/var(X2))))
lines(fest2[,1],fest2[,2]/var(X2),col=3,lwd=2)

CarolinaEuan/HMClust documentation built on Feb. 18, 2024, 10 p.m.