How to make density plot correctly show area near the limits?

Question

When I plot densities with ggplot, it seems to be very wrong around the limits. I see that geom_density and other functions allow specifying various density kernels, but none of them seem to fix the issue.

How do you correctly plot densities around the limits with ggplot?

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As an example, let's plot the Chi-square distribution with 2 degrees of freedom. Using the builtin probability densities:

library(ggplot2)

u = seq(0, 2, by=0.01)
v = dchisq(u, df=2)

df = data.frame(x=u, p=v)

p = ggplot(df) +
    geom_line(aes(x=x, y=p), size=1) +
    theme_classic() +
    coord_cartesian(xlim=c(0, 2), ylim=c(0, 0.5))

show(p)

We get the expected plot:

Now let's try simulating it and plotting the empirical distribution:

library(ggplot2)

u = rchisq(10000, df=2)

df = data.frame(x=u)

p = ggplot(df) +
    geom_density(aes(x=x)) +
    theme_classic() +
    coord_cartesian(xlim=c(0, 2))

show(p)

We get an incorrect plot:

We can try to visualize the actual distribution:

library(ggplot2, dplyr, tidyr)

u = rchisq(10000, df=2)

df = data.frame(x=u)

p = ggplot(df) +
    geom_point(aes(x=x, y=0.5), position=position_jitter(height=0.2), shape='.', alpha=1) +
    theme_classic() +
    coord_cartesian(xlim=c(0, 2), ylim=c(0, 1))

show(p)

And it seems to look correct, contrary to the density plot:

It seems like the problem has to do with kernels, and geom_density does allow using different kernels. But they don't really correct the limit problem. For example, the code above with triangular looks about the same:

Here's an idea of what I'm expecting to see (of course, I want a density, not a histogram):

library(ggplot2)

u = rchisq(10000, df=2)

df = data.frame(x=u)

p = ggplot(df) +
    geom_histogram(aes(x=x), center=0.1, binwidth=0.2, fill='white', color='black') +
    theme_classic() +
    coord_cartesian(xlim=c(0, 2))

show(p)

Answer 1

The usual kernel density methods have trouble when there is a constraint such as in this case for a density with only support above zero. The usual recommendation for handling this has been to use the logspline package:

install.packages("logspline")
library(logspline)
png(); fit <- logspline(rchisq(10000, 3))       
plot(fit) ; dev.off()

If this needed to be done in the ggplot2 environment there is a dlogspline function:

densdf <- data.frame( y=dlogspline(seq(0,12,length=1000), fit), 
                      x=seq(0,12,length=1000))

ggplot(densdf, aes(y=y,x=x))+geom_line()

Perhaps you were insisting on one with 2 degrees of freedom?