To plot a theoretical density over an empirical density

February 21, 2022

If I want to plot an empirical density, I would go:

library(ggplot2) ggplot() + geom_density(aes(x = rbeta(100,3,1)))

library(ggplot2)
ggplot() +
  geom_histogram(aes(x = rbeta(100,3,1)))

where rbeta(100,3,1) can be any vector.

If I want to plot a theoretical density, I could go:

library(ggplot2)
ggplot(data = data.frame(x = c(0, 1)), mapping = aes(x = x)) +
  stat_function(fun = dbeta, args = c(3,1), n = 100)

But when I try to plot the first curve over the second:

library(ggplot2)
ggplot(data = data.frame(x = c(0, 1)), mapping = aes(x = x)) +
  stat_function(fun = dbeta, args = c(3,1), n = 100) +
  geom_histogram(aes(x = rbeta(100,3,1)))

I will get an error.

How can I plot an empirically determined density over a theoretical?

>Solution :

This seems to work.
Plot the histogram first, then the density. And with more data points the histogram fits the theoretical density better.

library(ggplot2)
library(gridExtra)

set.seed(2022)

p1 <- ggplot() +
  geom_histogram(aes(x = rbeta(100,3,1), y = ..density..), bins = 30) +
  stat_function(fun = dbeta, args = c(3,1), n = 100)

p2 <- ggplot() +
  geom_histogram(aes(x = rbeta(10000,3,1), y = ..density..), bins = 30) +
  stat_function(fun = dbeta, args = c(3,1), n = 100)

grid.arrange(p1, p2, ncol=2)