100 exponential random variables and their relative likelihoods

exp_relative_likelihoods.R

suppressPackageStartupMessages({
  library(dplyr)
  library(ggplot2)
  library(purrr)
})
exp_likelihood <- function(x, lambda) {
  (lambda^length(x))*exp(-lambda*length(x)*mean(x))
}
seq_len(1e2) %>%
  lapply(function(i) {
    x <- rexp(100, rate = 3)
    lapply(seq(1, 5, 0.01),
           function(lambda) { exp_likelihood(x, lambda) }) %>% unlist() %>%
           { data.frame(lambda = seq(1, 5, 0.01), likelihood = .) } %>%
      mutate(rel_likelihood = likelihood / max(likelihood)) %>%
      mutate(boot = i)
  }) %>%
  bind_rows() %>%
  ggplot(aes(x = lambda, y = rel_likelihood)) +
  geom_line(aes(group = factor(boot)), 
            alpha = 0.3, size = 0.5) +
  theme_minimal() +
  ggtitle("100 exponential(rate = 3) relative likelihoods") +
  ylab("Relative likelihood estimates") +
  xlab("rate")