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I'm conducting some research where I need the critical values of the one-sample Kolmogorov-Smirnov distribution. I've found a number of tables online, but the answers from these tables seem too high. Here's one example; all the tables I find online agree with this one: https://www.soest.hawaii.edu/GG/FACULTY/ITO/GG413/K_S_Table_one_Sample.pdf

I wrote my own code in R to try and verify these values through simulation. The code is shown below:

ks_sim_crit <- function(n, alpha = .05, num_sims = 1000000) {

  ks_stat_vec <- numeric(num_sims)
  for(iter in seq(from = 1, to = num_sims, by = 1)) {

    iter_points <- runif(n = n)
    iter_ecdf <- ecdf(iter_points)
    ks_stat <- max(abs(iter_ecdf(iter_points) - iter_points))
    ks_stat_vec[iter] <- ks_stat

  }

  ks_stat_vec <- sort(ks_stat_vec)
  crit_val_index = round((1 - alpha) * num_sims)
  return(ks_stat_vec[crit_val_index])

}

When I run this code with n = 10 and the other default parameters I get a value of .377, where the table that I linked to suggests that the answer should be .409. Is there an error in my code or in the table?

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