Discrete stats fns

code.js

/**
 * @typedef Point
 * A pair of numbers suitable for plotting.
 */

/**
 * @param {Array.<number>} arr
 *        n observations of a continuous random variable (RV).
 * @returns {Array.<Point>}
 *        The empirical probabilities of the given observed values of the RV.
 *        @see https://en.wikipedia.org/wiki/Empirical_probability
 */
function emp(arr) {
  if (arr.length === 1) {
    return [[arr[0], 1]];
  }

  arr.sort();

  let result = [];
  let count = 1;
  for (let i = 1; i < arr.length; i++) {
    if (arr[i - 1] === arr[i]) {
      count++;
    }
    else {
      result.push([arr[i - 1], count / arr.length]);
      count = 1;
    }
  }

  // Get the last data point
  result.push([arr[arr.length - 1], count / arr.length]);

  return result;
}

test(emp, [3], [[3, 1]]);
test(emp, [1, 3, 2, 1, 2], [[1, 0.4], [2, 0.4], [3, 0.2]]);

/**
 * @param {Array.<number>} arr
 *        n observations of a continuous random variable (RV).
 * @returns {Array.<Point>}
 *        The empirical distribution function of the given observations.
 *        @see https://en.wikipedia.org/wiki/Empirical_distribution_function
 */
function edf(arr) {
  return emp(arr).reduce((acc, [value, prb], i) => {
    const firstPoint = (i === 0);
    const currentPrb = firstPoint ? prb : (acc[i - 1][1] + prb);
    acc.push([value, currentPrb]);
    return acc;
  }, []);
}

test(edf, [3], [[3, 1]]);
test(edf, [1, 3, 2, 1, 2], [[1, 0.4], [2, 0.8], [3, 1]]);


function arrEq(a1, a2) {
  if (a1.length !== a2.length) return false;
  return a1.every((_, i) => {
    // Be able to compare both array elements and number elements
    switch (typeof a1[i]) {
      case 'object': return arrEq(a1[i], a2[i]);
      case 'number': return a1[i] === a2[i];
    }
  })
}

function test(fn, arr, expected) {
  const actual = fn(arr);
  const match = arrEq(expected, actual);
  if (!match) throw new Error(`Expected ${expected}, got ${actual}`);
}