als-statistics/tests/table/cdft.test.js

A powerful and lightweight JavaScript library for descriptive statistics, regression, clustering, outlier detection, and noise analysis using a flexible table/column architecture.

const test = require('node:test');
const assert = require('node:assert');

const { gammaLn, betaLn, regularizedIncompleteBeta, tCDF } = require('../../lib/table/instruments/cdf');

function approxEqual(actual, expected, tolerance, message='') { 
  const diff = Math.abs(actual - expected);
  assert.ok(diff <= tolerance, `${message}\nactual=${actual}, expected=${expected}, diff=${diff}`);
}

test('gammaLn: проверка нескольких известных точек', () => {
  approxEqual(gammaLn(1), 0, 1e-14, 'lnGamma(1) должно быть ~0'); // 1) gamma(1) = 1 => ln(gamma(1)) = 0
  approxEqual(gammaLn(0.5), Math.log(Math.sqrt(Math.PI)), 1e-12, 'lnGamma(0.5) должно быть ln(sqrt(pi))'); // 2) gamma(1/2) = sqrt(pi) => lnGamma(1/2) = 0.5723649...    Для удобства округлим до ~7 знаков
  approxEqual(gammaLn(5), Math.log(24), 1e-12, 'lnGamma(5) должно быть ln(24)'); // 3) gamma(5) = 24 => ln(gamma(5)) = ln(24) = 3.1780538303...
});

test('betaLn: проверка известных значений Beta(a,b)', () => {
  approxEqual(betaLn(1,1), 0, 1e-14, 'betaLn(1,1) должно быть 0'); // 1) Beta(1,1)=1 => ln(Beta(1,1))=0
  approxEqual(betaLn(0.5, 0.5), Math.log(Math.PI), 1e-12, 'betaLn(0.5,0.5) должно быть ln(pi)'); // 2) Beta(0.5,0.5) = pi => ln(pi)=1.14472988585...
});

test('regularizedIncompleteBeta: несколько тестов I_x(a,b)', () => {
   approxEqual(regularizedIncompleteBeta(0.4, 2, 3), 0.5248, 1e-6, 'I_0.4(2,3) ~0.5248');
});

test('tCDF: проверка распределения Стьюдента', () => {
   approxEqual(tCDF(10, 1), 0.968274, 1e-6, 'tCDF(10; df=1) ~ 0.968274');
});