JavaScript Implementation of Error Function and Normal Cumulative Density Function

normal_cdf.js

// https://interactive.deolua.com/normal-dist

/*
*@param number 			x             - the value for which the cumulative probability value is desired
*@param number 			mean_val      - the value of the mean of the distribution
*@param number 			sd_val_sqrd   - the value of the SQUARE of the standard deviation of the distribution
*/

var normal_cdf = function(x, mean_val, sd_val_sqrd){
  var err_input = (x - mean_val)/(Math.sqrt(2 * sd_val_sqrd));
  
  return ((1/2) * (1 + err_function(err_input)));
};


// want to interact with more distribution and density functions in real time?
// Go here for more: https://interactive.deolua.com

normal_err.js

// https://interactive.deolua.com/normal-dist

// This is an implementation of one of the options of Abramowitz and Stegun's approximations:
// https://en.wikipedia.org/wiki/Error_function#Numerical_approximations

/*
*@param number 			x
*/

var err_function = function(x){
  if(x >= 0){
    var p = 0.47047, a1 = 0.3480242, a2 = -0.0958798, a3 = 0.7478556;
    var t = 1/(1 + (p * x));
    
    var expon_multi = Math.exp(-(x * x));
    
    var erf_result = 1 - ((t*(a1 + t*(a2 + t*(a3)))) * expon_multi);
    
    return erf_result;
  }
  else return (-err_function(-x));
};


// want to interact with more distribution and density functions in real time?
// Go here for more: https://interactive.deolua.com