JavaScript Program for Normal CDF Calculator

In this article, we will discuss a normal CDF calculator in JavaScript. A CDF calculator computes the Cumulative Distribution Function (CDF) for a given statistical variable. It indicates the probability that the variable’s value is less than or equal to a specified point, calculating the CDF is essential for understanding the probabilities associated with a normal distribution.

We will explore all the above methods along with their basic implementation with the help of examples.

Approach 1: Using the Error Function (erf)

Using the Error Function (erf) is a mathematical approach commonly employed to solve problems related to probability and statistics. The formula CDF(x) = 0.5 * (1 + erf(x / sqrt(2))) transforms input values into probabilities, aiding statistical analysis.

Syntax:

function name(x, mean, stdDev) 
{
    // code
};
  const z = (x - mean) / (stdDev * Math.sqrt(2));
  return 0.5 * (1 + erf(z));
}

Example: In this example, we are using the above-explained approach.

Javascript

function GFG(x) {
    const a1 = 0.48592;
    const a2 = -1.14736;
    const a3 = 2.52741;
    const a4 = -1.45527;
    const a5 = 4.256;
    const A = 0.37711;
    const s = (x < 0) ? -1 : 1;
    x = Math.abs(x) / Math.sqrt(2.0);
    const B = 1.0 / (1.0 + A * x);
    const C = 1.0 - (((((a5 * B + a4)
        * B + a3) * B + a2) * B + a1) * B)
        * Math.exp(-x * x);
    return 0.5 * (1.0 + s * C);
}
const Z = 1.5;
const D1 = GFG(Z);
console.log(`CDF at Z=${Z}: ${D1.toFixed(4)}`);

Output

CDF at Z=1.5: 0.8222

Approach 2: Using Taylor Series Expansion

Taylor series expansion approximates normal CDF. Calculate terms based on input x, coefficients, and constants. Return result or its complement for x > 0.

Syntax:

function GFG(x) {
    const T = 1 / (1 + 0.2316419 * Math.abs(x));
    const cd = D * T * (0.3193815 + T * (-0.3565638 + T * (1.781478 + T * (-1.821256 + T * 1.330274))));
    return cd;
};

Example : In this example we are using the above-explained approach.

Javascript

function GFG(x) {
    const T =
        1 / (1 + 0.2316419 * Math.abs(x));
    const D =
        0.3989423 * Math.exp(-x * x / 2);
    const cd =
        D * T * (0.3193815 + T * (-0.3565638 + T *
            (1.781478 + T * (-1.821256 + T * 1.330274))));
    if (x > 0) return 1 - cd;
    return cd;
}
console.log(GFG(1.5));

Output

0.9331927822029031