V8 Javascript that demonstrates the Central Limit Theorem

clt.js

// A large number to be used as infinite
var inf = 10000;

// The number of segments in which a continuous random variable is divided
// to get an aproximation in the discrete
var nSegments = 10;

// U ~ Uniform(0, 1)
function u() {
  return Math.random();
}

// X ~ Exponential(l)
function x(l) { 
  return - Math.log(1 - u()) / l;
}

// Take a sample {X1, X2, ... Xn}
function sample(n, distribution, params) {
  var s = [];
  while (s.length <= n) s.push(distribution.apply(null, params));
  return s;
}

// Calculate the frequency of each value in a sample (apply discretization)
function frequency(s) {
  var max = Math.max.apply(null, s);
  var min = Math.min.apply(null, s);
  var segmentSize = (max - min) / nSegments;
  var f = [];
  var segmentId;
  for (var j = 0; j < nSegments; j++) { 
    f[j] = 0; 
  }
  for (var i = 0; i < s.length; i++) {
    segmentId = Math.floor((s[i] - min) / segmentSize);
    f[segmentId] += 1;
  }
  return f;
}

function printSample(s) {
  var i, j, out = "";
  var f = frequency(s);
  for (i = 0; i < f.length; i++) {
    out += i + "\t";
    for (j = 0; j < f[i]; j++)
      out += "+";
    out += "\n";
  }
  print(out);
}

// Y = X1 + X2 + ... Xn => if n -> inf then Y ~ N(0, 1)
function y(n, iid, iidParams) {
  var s = sample(n, iid, iidParams);
  return s.reduce(function (sum, value) { return sum + value; }, 0);
}

// Main
var xParams = [0.2];

print("X sample");
var xSample1 = sample(100, x, xParams);
printSample(xSample1);

print("Y sample");
var ySample1 = sample(100, y, [inf, x, xParams]);
printSample(ySample1);