L1norm for piecewise linear functions
Intended to compute the L1norm of the difference between two distribution functions.
L1norm(F, G, eps = 1e-06)
F |
A stepfunction |
G |
Another stepfunction |
eps |
A tolerance parameter |
Both F and G should be of class stepfun, and they should be
non-defective distribution functions. There are some tolerance issues in
checking whether both functions are proper distribution functions at the
extremes of their support. For simulations it may be prudent to wrap
L1norm in try.
A real number.
R. Koenker
# Make a random step (distribution) function with Gaussian knots
rstep <- function(n){
x <- sort(rnorm(n))
y <- runif(n)
y <- c(0,cumsum(y/sum(y)))
stepfun(x,y)
}
F <- rstep(20)
G <- rstep(10)
S <- L1norm(F,G)
plot(F,main = paste("||F - G|| = ", round(S,4)))
lines(G,col = 2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.