distribution-mean-median-ratios.R

require(tidyverse)

mm_ratio = function(x) mean(x) / median(x)

x = map(10^seq(2,6,length.out = 200), ~ list(unif = runif(.x), exp = rexp(.x), log = rlnorm(.x)))

d = x %>% map_df(~ tibble(n = length(.x$unif), 
                          unif = mm_ratio(.x$unif), 
                          exp = mm_ratio(.x$exp), 
                          log = mm_ratio(.x$log)))

ds = d %>% pivot_longer(-n) %>% 
  filter(n > 100000) %>% 
  group_by(name) %>% summarise(value = mean(value))

d %>% pivot_longer(-n) %>% 
  ggplot(aes(n, value, col = name)) + 
  geom_point(size = .5, show.legend = FALSE) + geom_line(size = .3) + 
  geom_text(data = ds, aes(x = 1e6, y = value, label = round(value,3)), hjust = 0, nudge_x = 0.02, show.legend = FALSE) +
  scale_x_log10(labels = scales::comma, limits = c(100, 1300000)) + 
  labs(x = 'Array size', y = 'Ratio', title = 'Mean / Median ratio', col = 'Distribution') +
  theme(legend.position = 'top') +
  guides(colour = guide_legend(override.aes = list(size = 4)))+
  theme(legend.key=element_rect(fill=NA))