als-statistics/lib/table/instruments/cdf.js

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

const EPS = 3e-14;
const FPMIN = 1e-30;
const P = [676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7];
const G = 7;

function betacfNR(x, a, b) {
   const MAXIT = 200;
   let qab = a + b;
   let qap = a + 1;
   let qam = a - 1; // используется только для инициализации, но оставим для ясности
   let c = 1.0;
   let d = 1.0 - (qab * x) / qap;
   if (Math.abs(d) < FPMIN) d = FPMIN;
   d = 1.0 / d;
   let h = d;

   for (let m = 1; m <= MAXIT; m++) {
      const m2 = 2 * m;
      // Even step
      let aa = m * (b - m) * x / ((a + m2 - 1) * (a + m2));
      d = 1.0 + aa * d;
      if (Math.abs(d) < FPMIN) d = FPMIN;
      c = 1.0 + aa / c;
      if (Math.abs(c) < FPMIN) c = FPMIN;
      d = 1.0 / d;
      h *= (d * c);

      // Odd step
      aa = - (a + m) * (qab + m) * x / ((a + m2) * (a + m2 + 1));
      d = 1.0 + aa * d;
      if (Math.abs(d) < FPMIN) d = FPMIN;
      c = 1.0 + aa / c;
      if (Math.abs(c) < FPMIN) c = FPMIN;
      d = 1.0 / d;
      let delta = d * c;
      h *= delta;
      if (Math.abs(delta - 1.0) < EPS) {
         break;
      }
   }
   return h;
}

function gammaLn(z) {
   if (z < 0.5) return Math.log(Math.PI) - Math.log(Math.sin(Math.PI * z)) - gammaLn(1 - z);
   else {
      z -= 1;
      let x = 0.99999999999980993;
      for (let i = 0; i < P.length; i++) {
         x += P[i] / (z + i + 1);
      }
      const t = z + G + 0.5;
      return 0.5 * Math.log(2 * Math.PI) + (z + 0.5) * Math.log(t) - t + Math.log(x);
   }
}

function betaLn(a, b) { return gammaLn(a) + gammaLn(b) - gammaLn(a + b) }

function regularizedIncompleteBeta(x, a, b) {
   if (x <= 0) return 0;
   if (x >= 1) return 1;
   const bt = Math.exp(a * Math.log(x) + b * Math.log(1 - x) - betaLn(a, b));

   let sym = false;
   let xx = x, aa = a, bb = b;
   if (x > (a + 1) / (a + b + 2)) {
      sym = true;
      xx = 1 - x;
      aa = b;
      bb = a;
   }

   const cf = betacfNR(xx, aa, bb);
   let val = bt / aa * cf;
   if (sym) val = 1 - val;
   return val;
}

function tCDF(t, df) {
   if (df <= 0) throw new Error("Degrees of freedom must be positive");
   if (t === 0) return 0.5;

   const x = df / (df + t * t);
   const a = df / 2;
   const b = 0.5;

   const ibeta = regularizedIncompleteBeta(x, a, b);
   return (t >= 0) ? 1 - 0.5 * ibeta : 0.5 * ibeta;
}

module.exports = { gammaLn, betaLn, regularizedIncompleteBeta, tCDF };