Nonuniform Random Number Generators

A nice R feature that I haven’t seen in any other language is random number generators for distributions other than the uniform distribution. The most useful is the normal distribution: here’s a crude simulation of rnorm in ruby

def rnorm(mean=0, sd=1)
  coin_flips=37
  binomial = Array.new(coin_flips) { rand(2) }.inject { |m,o| m+o }
  zscore = 2 * (binomial - (coin_flips/2))/coin_flips**0.5
  zscore * sd + mean
end

and in javascript:

function rnorm(mean,sd) {
  coin_flips=37;
  if (null == mean) { mean = 0; }
  if (null == sd) { sd = 1;}
  binomial=0;
  for(i=0;i < coin_flips; i++) {
    if ( 0.5 < Math.random() ) {
      binomial += 1;
    }
  }
  zscore = 2 * (binomial - (coin_flips/2))/Math.pow(coin_flips,0.5);
  return zscore  * sd + mean;
}

Unlike the R version, there are only 38 possible values that above functions can assume, which might not be acceptable if repeated trials are being made. To fix that, here is a ruby version which mixes in another random number.

def fuzz(width)
  [(rand-0.5)*width, ((width**2)/12.0)**0.5]
end

def rnorm(mean=0, sd=1)
  coin_flips=37
  fuzz, fuzz_sd = fuzz(1/coin_flips**0.5)
  binomial = Array.new(coin_flips) { rand(2) }.inject { |m,o| m+o }
  zscore = 2 * (binomial - (coin_flips/2))/coin_flips**0.5
  zscore * (sd**2-fuzz_sd**2)**0.5 + mean + fuzz
end