simple-statistics/src/error_function.js

Simple Statistics

/**
 * **[Gaussian error function](http://en.wikipedia.org/wiki/Error_function)**
 *
 * The `errorFunction(x/(sd * Math.sqrt(2)))` is the probability that a value in a
 * normal distribution with standard deviation sd is within x of the mean.
 *
 * This function returns a numerical approximation to the exact value.
 * It uses Horner's method to evaluate the polynomial of τ (tau).
 *
 * @param {number} x input
 * @return {number} error estimation
 * @example
 * errorFunction(1).toFixed(2); // => '0.84'
 */
function errorFunction(x) {
    const t = 1 / (1 + 0.5 * Math.abs(x));
    const tau =
        t *
        Math.exp(
            -x * x +
                ((((((((0.17087277 * t - 0.82215223) * t + 1.48851587) * t -
                    1.13520398) *
                    t +
                    0.27886807) *
                    t -
                    0.18628806) *
                    t +
                    0.09678418) *
                    t +
                    0.37409196) *
                    t +
                    1.00002368) *
                    t -
                1.26551223
        );
    if (x >= 0) {
        return 1 - tau;
    } else {
        return tau - 1;
    }
}

export default errorFunction;