Nonuniform Random Number Generators II

According to the central limit theorem, a large enough sample from any distribution will converge to a normal distribution. So we might as well use the built in uniform distribution, which has variance 1/12, and the fact that the sum of independent random variables has variance equal to the sum of the variances.

def rnorm(mean=0, sd=1)
  n = 30
  sum = Array.new(n) { rand }.inject { |m,o| m+o }
  zscore = (sum - (n/2.0))/(n/12.0)**0.5
  zscore * sd + mean
end

How to make a quick ASCII histogram of the results:

h = Hash.new(0)
1000.times { h[(10*rnorm).to_i.to_f/10] += 1 }
(-35..35).each { |k| puts "#{k.abs/10.0} #{'#' * h[k/10.0]}" }

A javascript version:

function rnorm(mean,sd) {
  n=30;
  if (null == mean) { mean = 0; }
  if (null == sd) { sd = 1;}
  for(sum=0, i=0;i < n; i++) {
    sum += Math.random();
  }
  zscore = (sum - (n/2))/Math.pow(n/12,0.5);
  return zscore * sd + mean;
}

6/16 update: code fix: tripped up by the fact that 3/2 == 1 in ruby. In javascript 3/2 == 1.5