Cumulative distribution function in Javascript
The math.js library provides an erf
function. Based on a definition found at Wolfram Alpha , the cdfNormal
function 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
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); //-> 0.12651187738346226
//wolframalpha.com 0.12651200000000000