Calculates the overlapping area between normal distributions

overlapArea.ts

import NormalDistribution from "normal-distribution";

type TDistribution = Array<number>;

export function overlapArea(rating1: TDistribution, rating2: TDistribution) {
  const [mean1, sd1] = rating1;
  const [mean2, sd2] = rating2;

  const normalDistribution1 = new NormalDistribution(mean1, sd1);
  const normalDistribution2 = new NormalDistribution(mean2, sd2);

  const min = Math.min(mean1 - 6 * sd1, mean2 - 6 * sd2);
  const max = Math.max(mean1 + 6 * sd1, mean2 + 6 * sd2);
  const range = max - min;

  const resolution = range / Math.min(sd1, sd2);

  const partwidth = range / resolution;

  let intersectionArea = 0;

  const begin = (Math.max(mean1 - 6 * sd1, mean2 - 6 * sd2) - min) / partwidth;
  const end = (Math.min(mean1 + 6 * sd1, mean2 + 6 * sd2) - min) / partwidth;

  /// Divide the range into N partitions
  for (let ii = begin; ii < end; ii += 1) {
    const partMin = partwidth * ii;
    const partMax = partwidth * (ii + 1);

    const areaOfDist1 = normalDistribution1.probabilityBetween(
      partMin,
      partMax
    );
    const areaOfDist2 = normalDistribution2.probabilityBetween(
      partMin,
      partMax
    );

    intersectionArea += Math.min(areaOfDist1, areaOfDist2);
  }

  return intersectionArea;
}