Pairwise Measures for Two Sets of Empirical CDFs

We measure distance between two sets of empirical cumulative distribution functions (ECDF). For simplicity, we only take an input of ecdf objects from stats package.

ecdfdist2(elist1, elist2, method = c("KS", "Lp", "Wasserstein"), p = 2)

Arguments

elist1

a length \(M\) list of ecdf objects.

elist2

a length \(N\) list of ecdf objects.

method

name of the distance/dissimilarity measure. Case insensitive.

p

exponent for Lp or Wasserstein distance.

Value

an \((M\times N)\) matrix of pairwise distances.

See also

ecdf ecdfdist

Examples

# \donttest{
## toy example
#  first list : 10 of random and uniform distributions
mylist1 = list()
for (i in 1:10){ mylist1[[i]] = stats::ecdf(stats::rnorm(50, sd=2))}
for (i in 11:20){mylist1[[i]] = stats::ecdf(stats::runif(50, min=-5))}

#  second list : 15 uniform and random distributions
mylist2 = list()
for (i in 1:15){ mylist2[[i]] = stats::ecdf(stats::runif(50, min=-5))}
for (i in 16:30){mylist2[[i]] = stats::ecdf(stats::rnorm(50, sd=2))}

## compute Kolmogorov-Smirnov distance
dm2ks = ecdfdist2(mylist1, mylist2, method="KS")
dm2lp = ecdfdist2(mylist1, mylist2, method="lp")
dm2wa = ecdfdist2(mylist1, mylist2, method="wasserstein")
nrs   = nrow(dm2ks)

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3), pty="s")
image(dm2ks[,nrs:1], axes=FALSE, main="Kolmogorov-Smirnov")
image(dm2lp[,nrs:1], axes=FALSE, main="L2")
image(dm2wa[,nrs:1], axes=FALSE, main="Wasserstein")

par(opar)
# }