als-statistics/lib/analyze/cdf/index.js

Modular JS statistics toolkit for Node.js and the browser: descriptive stats, correlations (Pearson/Spearman/Kendall), t-tests & ANOVA (Student/Welch), reliability (Cronbach’s alpha), regression (linear/logistic), clustering (DBSCAN/HDBSCAN), and table/co

import { betacfNR } from './betacfNR.js';
import { gammaLn } from './gammaLn.js';
import { constants } from './constants.js';

export default class CDF {
   static constants = constants
   static regularizedIncompleteBeta(x, a, b) {
      const { constants } = CDF
      if (x <= 0) return 0; if (x >= 1) return 1;
      const betaLn = gammaLn(a, constants) + gammaLn(b, constants) - gammaLn(a + b, constants)
      const bt = Math.exp(a * Math.log(x) + b * Math.log(1 - x) - betaLn);
      let sym = false, xx = x, aa = a, bb = b;
      if (x > (a + 1) / (a + b + 2)) { sym = true; xx = 1 - x; aa = b; bb = a; }
      let val = bt / aa * betacfNR(xx, aa, bb, constants);
      if (sym) val = 1 - val;
      return val;
   }

   static t(t, df) { // tCDF
      if (df <= 0) throw new Error("Degrees of freedom must be positive");
      if (t === 0) return 0.5;
      const x = df / (df + t * t), a = df / 2, b = 0.5;
      const ibeta = CDF.regularizedIncompleteBeta(x, a, b);
      return (t >= 0) ? 1 - 0.5 * ibeta : 0.5 * ibeta;
   }

   static f(F, df1, df2) { // fCDF
      if (F < 0 || df1 <= 0 || df2 <= 0) throw new Error("Invalid input for F-distribution");
      const x = (df1 * F) / (df1 * F + df2), a = df1 / 2, b = df2 / 2;
      return CDF.regularizedIncompleteBeta(x, a, b);
   }

   static phi(x) { // standard normal CDF Φ(x)
      if (!Number.isFinite(x)) return x === Infinity ? 1 : x === -Infinity ? 0 : NaN;
      if (x > 8) return 1;   // далеко в правом хвосте
      if (x < -8) return 0;   // далеко в левом хвосте

      // Φ(x) = 0.5 * (1 + erf(x / sqrt(2))) аппроксимация erf по Abramowitz & Stegun 7.1.26 (ошибка ~1e-7)
      const y = Math.abs(x) / Math.SQRT2;
      const t = 1 / (1 + 0.3275911 * y);
      const a1 = 0.254829592, a2 = -0.284496736, a3 = 1.421413741, a4 = -1.453152027, a5 = 1.061405429;
      const poly = (((((a5 * t) + a4) * t) + a3) * t + a2) * t + a1;
      const erf_abs = 1 - poly * t * Math.exp(-y * y); // erf(|x|/√2), положительный
      const erf = x < 0 ? -erf_abs : erf_abs;
      return 0.5 * (1 + erf);
   }

}