Log Scale on Reverse Cumulative Distribution Plot in ggplot2

January 19, 2024

How can I make ggplot2 use a logarithmic scale on the y axis for a reverse CDF?

This works:

rnorm(64) %>%
  tibble(kbps = .) %>%
  ggplot() +
  stat_ecdf(aes(x = kbps, y = 1 - ..y..), pad=FALSE)

But this does not:

rnorm(64) %>%
  tibble(kbps = .) %>%
  ggplot() +
  stat_ecdf(aes(x = kbps, y = 1 - ..y..), pad=FALSE) +
  scale_y_log10()

    
Warning: NaNs produced
Warning: [38;5;232mTransformation introduced infinite values in continuous y-axis[39m
Warning: [38;5;232mRemoved 64 rows containing missing values (`geom_step()`).[39m

EDIT:

I want the outcome to look like this:

Image taken from: https://cacm.acm.org/magazines/2018/7/229031-always-measure-one-level-deeper/fulltext

>Solution :

There’s a couple of ways to do this. You could simply log manually and inverse transform the labels in scale_y_continuous

rnorm(64) %>%
  tibble(kbps = .) %>%
  ggplot() +
  stat_ecdf(aes(x = kbps, y = log10(1 - after_stat(y))), pad = FALSE) +
  scale_y_continuous('1 - cdf (log scale)', breaks = seq(-3, 0), 
                     labels = 10^(seq(-3, 0)),
                     limits = c(-3, 0)) +
  theme_bw()

Or precalculate 1 – ecdf and use scale_y_log10 with geom_step

tibble(kbps = rnorm(1000)) |> 
  arrange(kbps) |>
  mutate(ecdf = 1 - (row_number() - 1) / n()) %>%
  ggplot(aes(kbps, ecdf)) +
  geom_step() +
  scale_y_log10() +
  theme_bw()