Cumulative distribution function in Javascript

Question

I am searching for a way to calculate the Cumulative distribution function in Javascript. Are there classes which have implemented this? Do you have an idea to get this to work? It does not need to be 100% percent accurate but I need a good idea of the value.

http://en.wikipedia.org/wiki/Cumulative_distribution_function

Answer 1

I was able to write my own function with the help of Is there an easily available implementation of erf() for Python? and the knowledge from wikipedia.

The calculation is not 100% correct as it is just a approximation.

function normalcdf(mean, sigma, to) 
{
    var z = (to-mean)/Math.sqrt(2*sigma*sigma);
    var t = 1/(1+0.3275911*Math.abs(z));
    var a1 =  0.254829592;
    var a2 = -0.284496736;
    var a3 =  1.421413741;
    var a4 = -1.453152027;
    var a5 =  1.061405429;
    var erf = 1-(((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*Math.exp(-z*z);
    var sign = 1;
    if(z < 0)
    {
        sign = -1;
    }
    return (1/2)*(1+sign*erf);
}

normalcdf(30, 25, 1.4241); //-> 0.000223264606750539
//wolframalpha.com              0.000223221102572082

Answer 2

The math.js library provides an erf function. Based on a definition found at Wolfram Alpha , the cdfNormalfunction can be implemented like this in Javascript:

const mathjs = require('mathjs')

function cdfNormal (x, mean, standardDeviation) {
  return (1 - mathjs.erf((mean - x ) / (Math.sqrt(2) * standardDeviation))) / 2
}

In the node.js console:

> console.log(cdfNormal(5, 30, 25))
> 0.15865525393145707 // Equal to Wolfram Alpha's result at: https://sandbox.open.wolframcloud.com/app/objects/4935c1cb-c245-4d8d-9668-4d353ad714ec#sidebar=compute