illustrate CLS convergence for non-skewed and highly skewed random variables.

central_limit_theorem.R

compare_histograms <- function(sn) { 
  sample_means <- function(r,n) { sqrt(n)*rowMeans(matrix(r(n*10000), ncol=n)) }
  center_scale <- function(v) (v - mean(v))/sd(v)
  
  exp_sample <- center_scale(sample_means(rexp,  sn))
  unif_sample <- center_scale(sample_means(runif, sn)) 

  max_break = ceiling(max(c(unif_sample, exp_sample)))
  min_break = floor(min(c(unif_sample, exp_sample)))
  breaks = seq(min_break,max_break,length.out=(max_break-min_break)*8+1)
  hist(unif_sample, breaks=breaks, col=adjustcolor('green', alpha.f=0.5),  xlim=c(min_break,max_break))
  hist(exp_sample, breaks=breaks, col=adjustcolor('yellow', alpha.f=0.5), xlim=c(min_break,max_break), add=T)
}
compare_histograms(30)