sum_nth_power_deviations.js

import mean from "./mean.js";

/**
 * The sum of deviations to the Nth power.
 * When n=2 it's the sum of squared deviations.
 * When n=3 it's the sum of cubed deviations.
 *
 * @param {Array<number>} x
 * @param {number} n power
 * @returns {number} sum of nth power deviations
 *
 * @example
 * var input = [1, 2, 3];
 * // since the variance of a set is the mean squared
 * // deviations, we can calculate that with sumNthPowerDeviations:
 * sumNthPowerDeviations(input, 2) / input.length;
 */
function sumNthPowerDeviations(x, n) {
    const meanValue = mean(x);
    let sum = 0;
    let tempValue;
    let i;

    // This is an optimization: when n is 2 (we're computing a number squared),
    // multiplying the number by itself is significantly faster than using
    // the Math.pow method.
    if (n === 2) {
        for (i = 0; i < x.length; i++) {
            tempValue = x[i] - meanValue;
            sum += tempValue * tempValue;
        }
    } else {
        for (i = 0; i < x.length; i++) {
            sum += Math.pow(x[i] - meanValue, n);
        }
    }

    return sum;
}

export default sumNthPowerDeviations;