free-gaussian/lib/gaussian.js

A JavaScript model of a Gaussian distribution

(function(exports){

  // Complementary error function
  // From Numerical Recipes in C 2e p221
  var erfc = function(x) {
    var z = Math.abs(x);
    var t = 1 / (1 + z / 2);
    var r = t * Math.exp(-z * z - 1.26551223 + t * (1.00002368 +
            t * (0.37409196 + t * (0.09678418 + t * (-0.18628806 +
            t * (0.27886807 + t * (-1.13520398 + t * (1.48851587 +
            t * (-0.82215223 + t * 0.17087277)))))))))
    return x >= 0 ? r : 2 - r;
  };

  // Inverse complementary error function
  // From Numerical Recipes 3e p265
  var ierfc = function(x) {
    if (x >= 2) { return -100; }
    if (x <= 0) { return 100; }

    var xx = (x < 1) ? x : 2 - x;
    var t = Math.sqrt(-2 * Math.log(xx / 2));

    var r = -0.70711 * ((2.30753 + t * 0.27061) /
            (1 + t * (0.99229 + t * 0.04481)) - t);

    for (var j = 0; j < 2; j++) {
      var err = erfc(r) - xx;
      r += err / (1.12837916709551257 * Math.exp(-(r * r)) - r * err);
    }

    return (x < 1) ? r : -r;
  };

  // Construct a new distribution from the precision and precisionmean
  var fromPrecisionMean = function(precision, precisionmean) {
    return gaussian(precisionmean/precision, 1/precision);
  };

  // Models the normal distribution
  var Gaussian = function(mean, variance) {
    if (variance <= 0) {
      throw new Error('Variance must be > 0 (but was ' + variance + ')');
    }
    this.mean = mean;
    this.variance = variance;
    this.standardDeviation = Math.sqrt(variance);
  }
  // Probability density function
  Gaussian.prototype.pdf = function(x) {
    var m = this.standardDeviation * Math.sqrt(2 * Math.PI);
    var e = Math.exp(-Math.pow(x - this.mean, 2) / (2 * this.variance));
    return e / m;
  };
  // Cumulative density function
  Gaussian.prototype.cdf = function(x) {
    return 0.5 * erfc(-(x - this.mean) / (this.standardDeviation * Math.sqrt(2)));
  };
  // Add distribution of this and d
  Gaussian.prototype.add = function(d) {
    return gaussian(this.mean + d.mean, this.variance + d.variance);
  };
  // Subtract distribution of this and d
  Gaussian.prototype.sub = function(d) {
    return gaussian(this.mean - d.mean, this.variance + d.variance);
  };
  // Scales this distribution by constant c
  Gaussian.prototype.scale = function(c) {
    return gaussian(this.mean*c, this.variance*c*c);
  };
  Gaussian.prototype.mul = function(d) {
    if(typeof(d)==="number"){ return this.scale(d); }
    var precision = 1/this.variance;
    var dprecision = 1/d.variance;
    return fromPrecisionMean(precision+dprecision, 
      precision*this.mean+dprecision*d.mean);
  };
  Gaussian.prototype.div = function(d) {
    if(typeof(d)==="number"){ return this.scale(1/d); }
    var precision = 1/this.variance;
    var dprecision = 1/d.variance;
    return fromPrecisionMean(precision-dprecision, 
      precision*this.mean-dprecision*d.mean);
  };
  Gaussian.prototype.ppf = function(x) {
    return this.mean - this.standardDeviation * Math.sqrt(2) * ierfc(2 * x);
  };
  var gaussian = function(mean, variance){ return new Gaussian(mean, variance); };
  exports(gaussian);
})(typeof(exports)==='undefined'? function(f){this['gaussian']=f} : function(f){module.exports=f});