Binomial distributions

binomial_distributions.R

library(ggplot2)
library(dplyr)

probs <- seq(0.05, 0.95, each = 0.05)

df <- lapply(probs, rbinom, n = 100, size = 100) %>%
  unlist() %>%
  data.frame("successes" = .) %>%
  mutate(probs = rep(probs, each = 100))

df_annotate <- df %>%
  group_by(probs) %>%
  summarise(top = max(density(successes)$y),
            mid = density(successes)$x[which.max(density(successes)$y)])

ggplot(df, aes(x = successes, group = factor(probs), fill = probs)) +
  geom_density(alpha = 0.75, color = "white") +
  geom_text(aes(label = probs, x = mid, y = top), data = df_annotate,
            vjust = 0, nudge_y = 0.001, size = 3) +
  geom_segment(aes(x = mid, xend = mid, yend = top), y = 0, data = df_annotate,
               linetype = "dashed", size = 0.25, color = "white") +
  theme_bw(10) +
  scale_fill_gradient(low = "red", high = "lightgreen") +
  scale_y_continuous(expand = c(0, 0), limits = c(0, max(df_annotate$top) * 1.2)) +
  labs(x = "\n# of successes", y = "Density\n", fill = "Probability\nof success",
       title = "Simulated draws from binomial distributions")